Note that what you are trying to do is calculate the integer log2 of an integer,
#include <stdio.h>#include <stdlib.h>unsigned intLog2(unsigned long x){ unsigned long n = x; int bits = sizeof(x)*8; int step = 1; int k=0; for( step = 1; step < bits; ) { n |= (n >> step); step *= 2; ++k; } //printf("%ld %ld\n",x, (x - (n >> 1)) ); return(x - (n >> 1));}Observe that you can attempt to search more than 1 bit at a time.
unsigned intLog2_a(unsigned long x){ unsigned long n = x; int bits = sizeof(x)*8; int step = 1; int step2 = 0; //observe that you can move 8 bits at a time, and there is a pattern... //if( x>1<<step2+8 ) { step2+=8; //if( x>1<<step2+8 ) { step2+=8; //if( x>1<<step2+8 ) { step2+=8; //} //} //} for( step2=0; x>1L<<step2+8; ) { step2+=8; } //printf("step2 %d\n",step2); for( step = 0; x>1L<<(step+step2); ) { step+=1; //printf("step %d\n",step+step2); } printf("log2(%ld) %d\n",x,step+step2); return(step+step2);}This approach uses a binary search
unsigned intLog2_b(unsigned long x){ unsigned long n = x; unsigned int bits = sizeof(x)*8; unsigned int hbit = bits-1; unsigned int lbit = 0; unsigned long guess = bits/2; int found = 0; while ( hbit-lbit>1 ) { //printf("log2(%ld) %d<%d<%d\n",x,lbit,guess,hbit); //when value between guess..lbit if( (x<=(1L<<guess)) ) { //printf("%ld < 1<<%d %ld\n",x,guess,1L<<guess); hbit=guess; guess=(hbit+lbit)/2; //printf("log2(%ld) %d<%d<%d\n",x,lbit,guess,hbit); } //when value between hbit..guess //else if( (x>(1L<<guess)) ) { //printf("%ld > 1<<%d %ld\n",x,guess,1L<<guess); lbit=guess; guess=(hbit+lbit)/2; //printf("log2(%ld) %d<%d<%d\n",x,lbit,guess,hbit); } } if( (x>(1L<<guess)) ) ++guess; printf("log2(x%ld)=r%d\n",x,guess); return(guess);}Another binary search method, perhaps more readable,
unsigned intLog2_c(unsigned long x){ unsigned long v = x; unsigned int bits = sizeof(x)*8; unsigned int step = bits; unsigned int res = 0; for( step = bits/2; step>0; ) { //printf("log2(%ld) v %d >> step %d = %ld\n",x,v,step,v>>step); while ( v>>step ) { v>>=step; res+=step; //printf("log2(%ld) step %d res %d v>>step %ld\n",x,step,res,v); } step /= 2; } if( (x>(1L<<res)) ) ++res; printf("log2(x%ld)=r%ld\n",x,res); return(res);}And because you will want to test these,
int main(){ unsigned long int x = 3; for( x=2; x<1000000000; x*=2 ) { //printf("x %ld, x+1 %ld, log2(x+1) %d\n",x,x+1,Log2(x+1)); printf("x %ld, x+1 %ld, log2_a(x+1) %d\n",x,x+1,Log2_a(x+1)); printf("x %ld, x+1 %ld, log2_b(x+1) %d\n",x,x+1,Log2_b(x+1)); printf("x %ld, x+1 %ld, log2_c(x+1) %d\n",x,x+1,Log2_c(x+1)); } return(0);}