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# 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.

```c
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:

```c
#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;
}
```


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