位運算簡單舉例
阿新 • • 發佈：2019-01-08
return dwRet;
}
else{
return 0;
}
}
檢測一個無符號數是不為2^n-1(^為冪)： x&(x+1)
將最右側0位改為1位： x | (x+1)
二進位制補碼運算公式：
-x = ~x + 1 = ~(x-1)
~x = -x-1
-(~x) = x+1
~(-x) = x-1
x+y = x - ~y - 1 = (x|y)+(x&y)
x-y = x + ~y + 1 = (x|~y)-(~x&y)
x^y = (x|y)-(x&y)
x|y = (x&~y)+y
x&y = (~x|y)-~x
x==y: ~(x-y|y-x)
x!=y: x-y|y-x
x< y: (x-y)^((x^y)&((x-y)^x))
x<=y: (x|~y)&((x^y)|~(y-x))
x< y: (~x&y)|((~x|y)&(x-y))//無符號x,y比較
x<=y: (~x|y)&((x^y)|~(y-x))//無符號x,y比較
使用位運算的無分支程式碼：
計算絕對值
int abs( int x )
{
int y ;
y = x >> 31 ;
return (x^y)-y ;//or: (x+y)^y
}
符號函式：sign(x) = -1, x<0; 0, x == 0 ; 1, x > 0
int sign(int x)
{
return (x>>31) | (unsigned(-x))>>31 ;//x=-2^31時失敗(^為冪)
}
三值比較：cmp(x,y) = -1, x<y; 0, x==y; 1, x > y
int cmp( int x, int y )
{
return (x>y)-(x-y) ;
}
doz=x-y, x>=y; 0, x<y
int doz(int x, int y )
{
int d ;
d = x-y ;
return d & ((~(d^((x^y)&(d^x))))>>31) ;
}
int max(int x, int y )
{
int m ;
m = (x-y)>>31 ;
return y & m | x & ~m ;
}
不使用第三方交換x,y:
1.x ^= y ; y ^= x ; x ^= y ;
2.x = x+y ; y = x-y ; x = x-y ;
3.x = x-y ; y = y+x ; x = y-x ;
4.x = y-x ; x = y-x ; x = x+y ;
雙值交換:x = a, x==b; b, x==a//常規編碼為x = x==a ? b :a ;
1.x = a+b-x ;
2.x = a^b^x ;
下舍入到2的k次方的倍數:
1.x & ((-1)<<k)
2.(((unsigned)x)>>k)<<k
上舍入：
1. t = (1<<k)-1 ; x = (x+t)&~t ;
2.t = (-1)<<k ; x = (x-t-1)&t ;
位計數,統計1位的數量：
1.
int pop(unsigned x)
{
x = x-((x>>1)&0x55555555) ;
x = (x&0x33333333) + ((x>>2) & 0x33333333 ) ;
x = (x+(x>>4)) & 0x0f0f0f0f ;
x = x + (x>>8) ;
x = x + (x>>16) ;
return x & 0x0000003f ;
}
2.
int pop(unsigned x) {
static char table[256] = { 0,1,1,2, 1,2,2,3, ...., 6,7,7,8 } ;
return table[x&0xff]+table[(x>>8)&0xff]+table[(x>>16)&0xff]+table[(x>>24)] ;
}
奇偶性計算:
x = x ^ ( x>>1 ) ;
x = x ^ ( x>>2 ) ;
x = x ^ ( x>>4 ) ;
x = x ^ ( x>>8 ) ;
x = x ^ ( x>>16 ) ;
結果中位於x最低位，對無符號x,結果的第i位是原數第i位到最左側位的奇偶性
位反轉：
unsigned rev(unsigned x)
{
x = (x & 0x55555555) << 1 | (x>>1) & 0x55555555 ;
x = (x & 0x33333333) << 2 | (x>>2) & 0x33333333 ;
x = (x & 0x0f0f0f0f) << 4 | (x>>4) & 0x0f0f0f0f ;
x = (x<<24) | ((x&0xff00)<<8) | ((x>>8) & 0xff00) | (x>>24) ;
return x ;
}
遞增位反轉後的數：
unsigned inc_r(unsigned x)
{
unsigned m = 0x80000000 ;
x ^= m ;
if( (int)x >= 0 )
do { m >>= 1 ; x ^= m ; } while( x < m ) ;
return x ;
}
混選位：
abcd efgh ijkl mnop ABCD EFGH IJKL MNOP->aAbB cCdD eEfF gGhH iIjJ kKlL mMnN oOpP
unsigned ps(unsigned x)
{
unsigned t ;
t = (x ^ (x>>8)) & 0x0000ff00; x = x ^ t ^ (t<<8) ;
t = (x ^ (x>>4)) & 0x00f000f0; x = x ^ t ^ (t<<4) ;
t = (x ^ (x>>2)) & 0x0c0c0c0c; x = x ^ t ^ (t<<2) ;
t = (x ^ (x>>1)) & 0x22222222; x = x ^ t ^ (t<<1) ;
return x ;
}
位壓縮：
選擇並右移字x中對應於掩碼m的1位的位,如：compress(abcdefgh,01010101)=0000bdfh
compress_left(x,m)操作與此類似，但結果位在左邊: bdfh0000.
unsigned compress(unsigned x, unsigned m)
{
unsigned mk, mp, mv, t ;
int i ;
x &= m ;
mk = ~m << 1 ;
for( i = 0 ; i < 5 ; ++i ) {
mp = mk ^ ( mk << 1) ;
mp ^= ( mp << 2 ) ;
mp ^= ( mp << 4 ) ;
mp ^= ( mp << 8 ) ;
mp ^= ( mp << 16 ) ;
mv = mp & m ;
m = m ^ mv | (mv >> (1<<i) ) ;
t = x & mv ;
x = x ^ t | ( t >> ( 1<<i) ) ;
mk = mk & ~mp ;
}
return x ;
}
位置換：
用32個5位數表示從最低位開始的位的目標位置，結果是一個32*5的位矩陣，
將該矩陣沿次對角線轉置後用5個32位字p[5]存放。
SAG(x,m) = compress_left(x,m) | compress(x,~m) ;
準備工作：
void init( unsigned *p ) {
p[1] = SAG( p[1], p[0] ) ;
p[2] = SAG( SAG( p[2], p[0]), p[1] ) ;
p[3] = SAG( SAG( SAG( p[3], p[0] ), p[1]), p[2] ) ;
p[4] = SAG( SAG( SAG( SAG( p[4], p[0] ), p[1]) ,p[2]), p[3] ) ;
}
實際置換：
int rep( unsigned x ) {
x = SAG(x,p[0]);
x = SAG(x,p[1]);
x = SAG(x,p[2]);
x = SAG(x,p[3]);
x = SAG(x,p[4]);
return x ;
}
二進位制碼到GRAY碼的轉換:
unsigned B2G(unsigned B )
{
return B ^ (B>>1) ;
}
GRAY碼到二進位制碼:
unsigned G2B(unsigned G)
{
unsigned B ;
B = G ^ (G>>1) ;
B = G ^ (G>>2) ;
B = G ^ (G>>4) ;
B = G ^ (G>>8) ;
B = G ^ (G>>16) ;
return B ;
}
找出最左0位元組的位置:
int zbytel( unsigned x )
{
static cahr table[16] = { 4,3,2,2, 1,1,1,1, 0,0,0,0, 0,0,0,0 } ;
unsigned y ;
y = (x&0x7f7f7f7f) + 0x7f7f7f7f ;
y = ~(y|x|0x7f7f7f7f) ;
return table[y*0x00204081 >> 28] ;//乘法可用移位和加完成
}
}
else{
return 0;
}
}
檢測一個無符號數是不為2^n-1(^為冪)： x&(x+1)
將最右側0位改為1位： x | (x+1)
二進位制補碼運算公式：
-x = ~x + 1 = ~(x-1)
~x = -x-1
-(~x) = x+1
~(-x) = x-1
x+y = x - ~y - 1 = (x|y)+(x&y)
x-y = x + ~y + 1 = (x|~y)-(~x&y)
x^y = (x|y)-(x&y)
x|y = (x&~y)+y
x&y = (~x|y)-~x
x==y: ~(x-y|y-x)
x!=y: x-y|y-x
x< y: (x-y)^((x^y)&((x-y)^x))
x<=y: (x|~y)&((x^y)|~(y-x))
x< y: (~x&y)|((~x|y)&(x-y))//無符號x,y比較
x<=y: (~x|y)&((x^y)|~(y-x))//無符號x,y比較
使用位運算的無分支程式碼：
計算絕對值
int abs( int x )
{
int y ;
y = x >> 31 ;
return (x^y)-y ;//or: (x+y)^y
}
符號函式：sign(x) = -1, x<0; 0, x == 0 ; 1, x > 0
int sign(int x)
{
return (x>>31) | (unsigned(-x))>>31 ;//x=-2^31時失敗(^為冪)
}
三值比較：cmp(x,y) = -1, x<y; 0, x==y; 1, x > y
int cmp( int x, int y )
{
return (x>y)-(x-y) ;
}
doz=x-y, x>=y; 0, x<y
int doz(int x, int y )
{
int d ;
d = x-y ;
return d & ((~(d^((x^y)&(d^x))))>>31) ;
}
int max(int x, int y )
{
int m ;
m = (x-y)>>31 ;
return y & m | x & ~m ;
}
不使用第三方交換x,y:
1.x ^= y ; y ^= x ; x ^= y ;
2.x = x+y ; y = x-y ; x = x-y ;
3.x = x-y ; y = y+x ; x = y-x ;
4.x = y-x ; x = y-x ; x = x+y ;
雙值交換:x = a, x==b; b, x==a//常規編碼為x = x==a ? b :a ;
1.x = a+b-x ;
2.x = a^b^x ;
下舍入到2的k次方的倍數:
1.x & ((-1)<<k)
2.(((unsigned)x)>>k)<<k
上舍入：
1. t = (1<<k)-1 ; x = (x+t)&~t ;
2.t = (-1)<<k ; x = (x-t-1)&t ;
位計數,統計1位的數量：
1.
int pop(unsigned x)
{
x = x-((x>>1)&0x55555555) ;
x = (x&0x33333333) + ((x>>2) & 0x33333333 ) ;
x = (x+(x>>4)) & 0x0f0f0f0f ;
x = x + (x>>8) ;
x = x + (x>>16) ;
return x & 0x0000003f ;
}
2.
int pop(unsigned x) {
static char table[256] = { 0,1,1,2, 1,2,2,3, ...., 6,7,7,8 } ;
return table[x&0xff]+table[(x>>8)&0xff]+table[(x>>16)&0xff]+table[(x>>24)] ;
}
奇偶性計算:
x = x ^ ( x>>1 ) ;
x = x ^ ( x>>2 ) ;
x = x ^ ( x>>4 ) ;
x = x ^ ( x>>8 ) ;
x = x ^ ( x>>16 ) ;
結果中位於x最低位，對無符號x,結果的第i位是原數第i位到最左側位的奇偶性
位反轉：
unsigned rev(unsigned x)
{
x = (x & 0x55555555) << 1 | (x>>1) & 0x55555555 ;
x = (x & 0x33333333) << 2 | (x>>2) & 0x33333333 ;
x = (x & 0x0f0f0f0f) << 4 | (x>>4) & 0x0f0f0f0f ;
x = (x<<24) | ((x&0xff00)<<8) | ((x>>8) & 0xff00) | (x>>24) ;
return x ;
}
遞增位反轉後的數：
unsigned inc_r(unsigned x)
{
unsigned m = 0x80000000 ;
x ^= m ;
if( (int)x >= 0 )
do { m >>= 1 ; x ^= m ; } while( x < m ) ;
return x ;
}
混選位：
abcd efgh ijkl mnop ABCD EFGH IJKL MNOP->aAbB cCdD eEfF gGhH iIjJ kKlL mMnN oOpP
unsigned ps(unsigned x)
{
unsigned t ;
t = (x ^ (x>>8)) & 0x0000ff00; x = x ^ t ^ (t<<8) ;
t = (x ^ (x>>4)) & 0x00f000f0; x = x ^ t ^ (t<<4) ;
t = (x ^ (x>>2)) & 0x0c0c0c0c; x = x ^ t ^ (t<<2) ;
t = (x ^ (x>>1)) & 0x22222222; x = x ^ t ^ (t<<1) ;
return x ;
}
位壓縮：
選擇並右移字x中對應於掩碼m的1位的位,如：compress(abcdefgh,01010101)=0000bdfh
compress_left(x,m)操作與此類似，但結果位在左邊: bdfh0000.
unsigned compress(unsigned x, unsigned m)
{
unsigned mk, mp, mv, t ;
int i ;
x &= m ;
mk = ~m << 1 ;
for( i = 0 ; i < 5 ; ++i ) {
mp = mk ^ ( mk << 1) ;
mp ^= ( mp << 2 ) ;
mp ^= ( mp << 4 ) ;
mp ^= ( mp << 8 ) ;
mp ^= ( mp << 16 ) ;
mv = mp & m ;
m = m ^ mv | (mv >> (1<<i) ) ;
t = x & mv ;
x = x ^ t | ( t >> ( 1<<i) ) ;
mk = mk & ~mp ;
}
return x ;
}
位置換：
用32個5位數表示從最低位開始的位的目標位置，結果是一個32*5的位矩陣，
將該矩陣沿次對角線轉置後用5個32位字p[5]存放。
SAG(x,m) = compress_left(x,m) | compress(x,~m) ;
準備工作：
void init( unsigned *p ) {
p[1] = SAG( p[1], p[0] ) ;
p[2] = SAG( SAG( p[2], p[0]), p[1] ) ;
p[3] = SAG( SAG( SAG( p[3], p[0] ), p[1]), p[2] ) ;
p[4] = SAG( SAG( SAG( SAG( p[4], p[0] ), p[1]) ,p[2]), p[3] ) ;
}
實際置換：
int rep( unsigned x ) {
x = SAG(x,p[0]);
x = SAG(x,p[1]);
x = SAG(x,p[2]);
x = SAG(x,p[3]);
x = SAG(x,p[4]);
return x ;
}
二進位制碼到GRAY碼的轉換:
unsigned B2G(unsigned B )
{
return B ^ (B>>1) ;
}
GRAY碼到二進位制碼:
unsigned G2B(unsigned G)
{
unsigned B ;
B = G ^ (G>>1) ;
B = G ^ (G>>2) ;
B = G ^ (G>>4) ;
B = G ^ (G>>8) ;
B = G ^ (G>>16) ;
return B ;
}
找出最左0位元組的位置:
int zbytel( unsigned x )
{
static cahr table[16] = { 4,3,2,2, 1,1,1,1, 0,0,0,0, 0,0,0,0 } ;
unsigned y ;
y = (x&0x7f7f7f7f) + 0x7f7f7f7f ;
y = ~(y|x|0x7f7f7f7f) ;
return table[y*0x00204081 >> 28] ;//乘法可用移位和加完成
}