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Optimization 确定字节中最重要设置位的位置

optimization

Optimization 确定字节中最重要设置位的位置,optimization,bit-manipulation,bitflags,Optimization,Bit Manipulation,Bitflags,我有一个字节用于存储位标志。我需要计算字节中最高有效位的位置 示例字节：00101101=>6是最高有效设置位的位置 压缩十六进制映射： [0x00] => 0x00 [0x01] => 0x01 [0x02,0x03] => 0x02 [0x04,0x07] => 0x03 [0x08,0x0F] => 0x04 [0x10,0x1F] => 0x05 [0x20,0x3F] => 0x06 [0x40,0x7F] => 0x

我有一个
字节
用于存储位标志。我需要计算字节中最高有效位的位置

示例字节：
00
1
01101
=>
6
是最高有效设置位的位置

压缩十六进制映射：

[0x00]      => 0x00
[0x01]      => 0x01
[0x02,0x03] => 0x02
[0x04,0x07] => 0x03
[0x08,0x0F] => 0x04
[0x10,0x1F] => 0x05
[0x20,0x3F] => 0x06
[0x40,0x7F] => 0x07
[0x80,0xFF] => 0x08

#include <stdio.h>

unsigned char check(unsigned char b) {
  unsigned char c = 0x08;
  unsigned char m = 0x80;
  do {
    if(m&b) { return  c; }
    else    { c -= 0x01; }
  } while(m>>=1);
  return 0; //never reached
}
int main() {
  unsigned char input[256] = {
    0x00,0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,
    0x10,0x11,0x12,0x13,0x14,0x15,0x16,0x17,0x18,0x19,0x1a,0x1b,0x1c,0x1d,0x1e,0x1f,
    0x20,0x21,0x22,0x23,0x24,0x25,0x26,0x27,0x28,0x29,0x2a,0x2b,0x2c,0x2d,0x2e,0x2f,
    0x30,0x31,0x32,0x33,0x34,0x35,0x36,0x37,0x38,0x39,0x3a,0x3b,0x3c,0x3d,0x3e,0x3f,
    0x40,0x41,0x42,0x43,0x44,0x45,0x46,0x47,0x48,0x49,0x4a,0x4b,0x4c,0x4d,0x4e,0x4f,
    0x50,0x51,0x52,0x53,0x54,0x55,0x56,0x57,0x58,0x59,0x5a,0x5b,0x5c,0x5d,0x5e,0x5f,
    0x60,0x61,0x62,0x63,0x64,0x65,0x66,0x67,0x68,0x69,0x6a,0x6b,0x6c,0x6d,0x6e,0x6f,
    0x70,0x71,0x72,0x73,0x74,0x75,0x76,0x77,0x78,0x79,0x7a,0x7b,0x7c,0x7d,0x7e,0x7f,
    0x80,0x81,0x82,0x83,0x84,0x85,0x86,0x87,0x88,0x89,0x8a,0x8b,0x8c,0x8d,0x8e,0x8f,
    0x90,0x91,0x92,0x93,0x94,0x95,0x96,0x97,0x98,0x99,0x9a,0x9b,0x9c,0x9d,0x9e,0x9f,
    0xa0,0xa1,0xa2,0xa3,0xa4,0xa5,0xa6,0xa7,0xa8,0xa9,0xaa,0xab,0xac,0xad,0xae,0xaf,
    0xb0,0xb1,0xb2,0xb3,0xb4,0xb5,0xb6,0xb7,0xb8,0xb9,0xba,0xbb,0xbc,0xbd,0xbe,0xbf,
    0xc0,0xc1,0xc2,0xc3,0xc4,0xc5,0xc6,0xc7,0xc8,0xc9,0xca,0xcb,0xcc,0xcd,0xce,0xcf,
    0xd0,0xd1,0xd2,0xd3,0xd4,0xd5,0xd6,0xd7,0xd8,0xd9,0xda,0xdb,0xdc,0xdd,0xde,0xdf,
    0xe0,0xe1,0xe2,0xe3,0xe4,0xe5,0xe6,0xe7,0xe8,0xe9,0xea,0xeb,0xec,0xed,0xee,0xef,
    0xf0,0xf1,0xf2,0xf3,0xf4,0xf5,0xf6,0xf7,0xf8,0xf9,0xfa,0xfb,0xfc,0xfd,0xfe,0xff };

  unsigned char truth[256] = {
    0x00,0x01,0x02,0x02,0x03,0x03,0x03,0x03,0x04,0x04,0x04,0x04,0x04,0x04,0x04,0x04, 
    0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05, 
    0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06, 
    0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06, 
    0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07, 
    0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07, 
    0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07, 
    0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07, 
    0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,
    0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,
    0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,
    0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,
    0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,
    0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,
    0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,
    0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08};

  int i,r;
  int f = 0;
  for(i=0; i<256; ++i) {
    r=check(input[i]);
    if(r !=(truth[i])) {
      printf("failed %d : 0x%x : %d\n",i,0x000000FF & ((int)input[i]),r);
      f += 1;
    }
  }
  if(!f) { printf("passed all\n");  }
  else   { printf("failed %d\n",f); }
  return 0;
}
C语言中的测试用例：

[0x00]      => 0x00
[0x01]      => 0x01
[0x02,0x03] => 0x02
[0x04,0x07] => 0x03
[0x08,0x0F] => 0x04
[0x10,0x1F] => 0x05
[0x20,0x3F] => 0x06
[0x40,0x7F] => 0x07
[0x80,0xFF] => 0x08

#include <stdio.h>

unsigned char check(unsigned char b) {
  unsigned char c = 0x08;
  unsigned char m = 0x80;
  do {
    if(m&b) { return  c; }
    else    { c -= 0x01; }
  } while(m>>=1);
  return 0; //never reached
}
int main() {
  unsigned char input[256] = {
    0x00,0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,
    0x10,0x11,0x12,0x13,0x14,0x15,0x16,0x17,0x18,0x19,0x1a,0x1b,0x1c,0x1d,0x1e,0x1f,
    0x20,0x21,0x22,0x23,0x24,0x25,0x26,0x27,0x28,0x29,0x2a,0x2b,0x2c,0x2d,0x2e,0x2f,
    0x30,0x31,0x32,0x33,0x34,0x35,0x36,0x37,0x38,0x39,0x3a,0x3b,0x3c,0x3d,0x3e,0x3f,
    0x40,0x41,0x42,0x43,0x44,0x45,0x46,0x47,0x48,0x49,0x4a,0x4b,0x4c,0x4d,0x4e,0x4f,
    0x50,0x51,0x52,0x53,0x54,0x55,0x56,0x57,0x58,0x59,0x5a,0x5b,0x5c,0x5d,0x5e,0x5f,
    0x60,0x61,0x62,0x63,0x64,0x65,0x66,0x67,0x68,0x69,0x6a,0x6b,0x6c,0x6d,0x6e,0x6f,
    0x70,0x71,0x72,0x73,0x74,0x75,0x76,0x77,0x78,0x79,0x7a,0x7b,0x7c,0x7d,0x7e,0x7f,
    0x80,0x81,0x82,0x83,0x84,0x85,0x86,0x87,0x88,0x89,0x8a,0x8b,0x8c,0x8d,0x8e,0x8f,
    0x90,0x91,0x92,0x93,0x94,0x95,0x96,0x97,0x98,0x99,0x9a,0x9b,0x9c,0x9d,0x9e,0x9f,
    0xa0,0xa1,0xa2,0xa3,0xa4,0xa5,0xa6,0xa7,0xa8,0xa9,0xaa,0xab,0xac,0xad,0xae,0xaf,
    0xb0,0xb1,0xb2,0xb3,0xb4,0xb5,0xb6,0xb7,0xb8,0xb9,0xba,0xbb,0xbc,0xbd,0xbe,0xbf,
    0xc0,0xc1,0xc2,0xc3,0xc4,0xc5,0xc6,0xc7,0xc8,0xc9,0xca,0xcb,0xcc,0xcd,0xce,0xcf,
    0xd0,0xd1,0xd2,0xd3,0xd4,0xd5,0xd6,0xd7,0xd8,0xd9,0xda,0xdb,0xdc,0xdd,0xde,0xdf,
    0xe0,0xe1,0xe2,0xe3,0xe4,0xe5,0xe6,0xe7,0xe8,0xe9,0xea,0xeb,0xec,0xed,0xee,0xef,
    0xf0,0xf1,0xf2,0xf3,0xf4,0xf5,0xf6,0xf7,0xf8,0xf9,0xfa,0xfb,0xfc,0xfd,0xfe,0xff };

  unsigned char truth[256] = {
    0x00,0x01,0x02,0x02,0x03,0x03,0x03,0x03,0x04,0x04,0x04,0x04,0x04,0x04,0x04,0x04, 
    0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05, 
    0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06, 
    0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06, 
    0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07, 
    0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07, 
    0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07, 
    0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07, 
    0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,
    0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,
    0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,
    0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,
    0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,
    0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,
    0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,
    0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08};

  int i,r;
  int f = 0;
  for(i=0; i<256; ++i) {
    r=check(input[i]);
    if(r !=(truth[i])) {
      printf("failed %d : 0x%x : %d\n",i,0x000000FF & ((int)input[i]),r);
      f += 1;
    }
  }
  if(!f) { printf("passed all\n");  }
  else   { printf("failed %d\n",f); }
  return 0;
}

#包括
无符号字符检查（无符号字符b）{
无符号字符c=0x08；
无符号字符m=0x80；
做{
if（m&b）{return c；}
else{c-=0x01；}
}而（m>>=1）；
返回0；//从未到达
}
int main（）{
无符号字符输入[256]={
0x00、0x01、0x02、0x03、0x04、0x05、0x06、0x07、0x08、0x09、0x0a、0x0b、0x0c、0x0d、0x0e、0x0f、，
0x10、0x11、0x12、0x13、0x14、0x15、0x16、0x17、0x18、0x19、0x1a、0x1b、0x1c、0x1d、0x1e、0x1f、，
0x20、0x21、0x22、0x23、0x24、0x25、0x26、0x27、0x28、0x29、0x2a、0x2b、0x2c、0x2d、0x2e、0x2f，
0x30、0x31、0x32、0x33、0x34、0x35、0x36、0x37、0x38、0x39、0x3a、0x3b、0x3c、0x3d、0x3e、0x3f、，
0x40、0x41、0x42、0x43、0x44、0x45、0x46、0x47、0x48、0x49、0x4a、0x4b、0x4c、0x4d、0x4e、0x4f、，
0x50、0x51、0x52、0x53、0x54、0x55、0x56、0x57、0x58、0x59、0x5a、0x5b、0x5c、0x5d、0x5e、0x5f、，
0x60、0x61、0x62、0x63、0x64、0x65、0x66、0x67、0x68、0x69、0x6a、0x6b、0x6c、0x6d、0x6e、0x6f、，
0x70、0x71、0x72、0x73、0x74、0x75、0x76、0x77、0x78、0x79、0x7a、0x7b、0x7c、0x7d、0x7e、0x7f、，
0x80、0x81、0x82、0x83、0x84、0x85、0x86、0x87、0x88、0x89、0x8a、0x8b、0x8c、0x8d、0x8e、0x8f、，
0x90、0x91、0x92、0x93、0x94、0x95、0x96、0x97、0x98、0x99、0x9a、0x9b、0x9c、0x9d、0x9e、0x9f、，
0xa0,0xa1,0xa2,0xa3,0xa4,0xa5,0xa6,0xa7,0xa8,0xa9,0xaa,0xab,0xac,0xad,0xae,0xaf，
0xb0，0xb1，0xb2，0xb3，0xb4，0xb5，0xb6，0xb7，0xb8，0xb9，0xba，0xbb，0xbc，0xbd，0xbe，0xbf，
0xc0，0xc1，0xc2，0xc3，0xc4，0xc5，0xc6，0xc7，0xc8，0xc9，0xca，0xcb，0xcc，0xcd，0xce，0xcf，
0xd0，0xd1，0xd2，0xd3，0xd4，0xd5，0xd6，0xd7，0xd8，0xd9，0xda，0xdb，0xdc，0xdd，0xde，0xdf，
0xe0，0xe1，0xe2，0xe3，0xe4，0xe5，0xe6，0xe7，0xe8，0xe9，0xea，0xeb，0xec，0xed，0xee，0xef，
0xf0、0xf1、0xf2、0xf3、0xf4、0xf5、0xf6、0xf7、0xf8、0xf9、0xfa、0xfb、0xfc、0xfd、0xfe、0xff}；
无符号字符真值[256]={
0x00,0x01,0x02,0x02,0x03,0x03,0x03,0x04,0x04,0x04,0x04,0x04,0x04,0x04,0x04,0x04,0x04,0x04，
0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05,0x05，
0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06，
0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06,0x06，
0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07，
0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07，
0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07，
0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07,0x07，
0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08，
0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08，
0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08，
0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08，
0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08，
0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08，
0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08，
0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08,0x08}；
int i，r；
int f=0；

对于（i=0；i在普通C中是不可能的。我建议最好的方法是执行下面的check。尽管非常“丑陋”，但我认为它比问题中的ckeck版本运行得更快


int check(unsigned char b)
{
    if(b&128) return 8;
    if(b&64)  return 7;
    if(b&32)  return 6;
    if(b&16)  return 5;
    if(b&8)   return 4;
    if(b&4)   return 3;
    if(b&2)   return 2;
    if(b&1)   return 1;
              return 0;
}



这在普通C语言中是不可能的。我建议最好的方法是执行下面的check。尽管相当“丑陋”，但我认为它比问题中的ckeck版本运行得更快


int check(unsigned char b)
{
    if(b&128) return 8;
    if(b&64)  return 7;
    if(b&32)  return 6;
    if(b&16)  return 5;
    if(b&8)   return 4;
    if(b&4)   return 3;
    if(b&2)   return 2;
    if(b&1)   return 1;
              return 0;
}


编辑：我找到了一个指向实际代码的链接：
下面的算法在该文件中命名为
nlz8
。你可以选择你最喜欢的黑客

Edit——不完全确定asker所说的独立于语言是什么意思，但下面是python中的等效代码

编辑：我找到了一个指向实际代码的链接：
下面的算法在该文件中命名为
nlz8
。你可以选择你最喜欢的黑客

Edit——不完全确定asker所说的独立于语言是什么意思，但下面是python中的等效代码


你的问题是关于一种有效的方法来计算一个值的
log2
，因为你似乎想要一个不局限于C语言的解决方案，所以我有点懒，并调整了一些C代码

您希望计算
log2（x）+1
，对于
x=0
（其中
log2
未定义），您将结果定义为0（例如，您创建了一个特殊情况，其中
log2（0）=-1
）

这一位旋转黑客是从你可以看到相当于C源代码的32位值。这段代码已被改编为工作在8位值

但是，您可以使用一个操作，该操作使用一个非常高效的内置函数（在许多CPU上使用的是一条指令，如）。该问题的答案包含一些有关此问题的信息。答案中的引用提供了解决此问题的低级别支持的一个可能原因：

这样的事情是许多O（1）算法的核心，比如内核调度器，它需要找到由位数组表示的第一个非空队列


你的问题是关于一种有效的方法来计算一个值的
log2
，因为你似乎想要一个不局限于C语言的解决方案，所以我有点懒，并调整了一些C代码

您希望计算
log2（x）+1
，对于
x=0
（其中
log2
未定义），您将结果定义为0（例如，您创建了一个特殊情况w

static unsigned char check(unsigned char b)
{
  unsigned char r = 8;
  unsigned char sub = 1;
  unsigned char s = 7;
  for (char i = 0; i < 8; i++)
  {
      sub = sub & ((( b & (1 << s)) >> s--) - 1);
      r -= sub;
  }
  return r;
}



  Pseudo-code:

  // see if there's a bit set in the upper half   
  if ((b >> 4) != 0)  
  {
      offset = 4;
      b >>= 4;   
  }   
  else
      offset = 0;

  // see if there's a bit set in the upper half of what's left   
  if ((b & 0x0C) != 0)   
  {
    offset += 2;
    b >>= 2;   
  }

  // see if there's a bit set in the upper half of what's left   
  if > ((b & 0x02) != 0)   
  {
    offset++;
    b >>= 1;   
  }

  return b + offset;



static unsigned char check(unsigned char b)
{    
  unsigned char adj = 4 & ((((unsigned char) - (b >> 4) >> 7) ^ 1) - 1);
  unsigned char offset = adj;
  b >>= adj;
  adj = 2 & (((((unsigned char) - (b & 0x0C)) >> 7) ^ 1) - 1);
  offset += adj;
  b >>= adj;
  adj = 1 & (((((unsigned char) - (b & 0x02)) >> 7) ^ 1) - 1);
  return (b >> adj) + offset + adj;
}