CSAPP (1): Computer Representation of numbers-after-school questions, after-school csapp

CSAPP (1): Computer Representation of numbers-after-school questions, after-school csapp

2.65

Int even_ones (unsigned x)

Requirement: return 1 when x contains an even number of 1 s; 0 otherwise. Assume that int has w = 32 bits.

Analysis: the loop statement is not applicable. If you write a statement one by one, it will take 32 times; here, the operation is changed to logstores = 5 times. The bipartite method implies loop while simplifying loop traversal. How does one use the bipartite method?

The question is to judge the parity of 1 in x. We can divide x into 2. For example, if the first 16-bit x1 and the last 16-bit x2, x3 = x1 ^ x2, then, if x has an even number of 1, x3 must have an even number of 1; if x has an odd number of 1, x3 must have an odd number.

int even_ones(unsigned x){     x ^= (x >> 16);     x ^= (x >> 8);     x ^= (x >> 4);     x ^= (x >> 2);     x ^= (x >> 1);     return !(x & 1);    }

 

2.66

Int leftmost_one (unsigned x)

Requirements: generate mask indicating leftmost 1 in x. assume w = 32; if x = 0, then return 0;

Tip: Convert x into a bit vector like [0 .. 011 .. 1 ].

Analysis: here we look for the first bit of the highest bit of 1 in the vector x, we should use a loop, and then the loop is not available, here we use a bipartite. First, as in [tip], convert x to a bit vector like [0 .. 011 .. 1], that is, all the bits after the highest bit 1 are changed to 1.

int leftmost_one(unsigned x){     x |= x >> 1;     x |= x >> 2;     x |= x >> 4;     x |= x >> 8;     x |= x >> 16;     x &= ~(x >> 1);     return x;}