2.84 Float Le

★★

Problem:

Fill in the return value for the following procedure, which tests whether its first argument is less than or equal to its second. Assume the function f2u returns an unsigned 32-bit number having the same bit representation as its floating-point argument. You can assume that neither argument is NaN. The two flavors of zero, +0 and -0, are considered equal.

int float_le(float x, float y) {
    unsigned ux = f2u(x);
    unsigned uy = f2u(y);
    /* Get the sign bits */
    unsigned sx = ux >> 31;
    unsigned sy = uy >> 31;

    /* Give an expression using only ux, uy, sx, and sy */
    return ____;
}

Code:

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

unsigned f2u(float x) {
    return *(unsigned *)&x;
}

int float_le(float x, float y) {
    unsigned ux = f2u(x);
    unsigned uy = f2u(y);
    /* Get the sign bits */
    unsigned sx = ux >> 31;
    unsigned sy = uy >> 31;

    /* Give an expression using only ux, uy, sx, and sy */
    return (ux << 1 == 0 && uy << 1 == 0) ||    /* both x and y equal to 0 */
        (sx && !sy) ||    /* x<0 and y>0 */
        (sx && sy && ux >= uy) ||
        (!sx && !sy && ux <= uy);
}

int main() {
    assert(float_le(-0.0, +0.0));
    assert(float_le(-3.0, 1.0));
    assert(float_le(-4.0, -3.0));
    assert(float_le(1.0, 2.0));
    return 0;
}