Question

1 :float Q_rsqrt( float number )
2 :{
3 :    int32_t i;
4 :    float x2, y;
5 :    const float threehalfs = 1.5F;
6 :
7 :    x2 = number * 0.5F;
8 :    y = number;
9 :    i = * ( int32_t * ) &y; // evil floating point bit level hacking
10:    i = 0x5f3759df - ( i >> 1 ); // what the hugs? 
11:    y = * ( float * ) &i;
12:    y = y * ( threehalfs - ( x2 * y * y ) ); // 1st iteration, newton's approximation
13:    // y = y * ( threehalfs - ( x2 * y * y ) ); // 2nd iteration, this can be removed
14:
15:    return y;
16:}

For the variable evaluated in part 6, if the bit pattern is evaluated as an IEEE 32-bit floating-point number, what is the value of this number in decimal?

Part 6:

Given that number=0.15625, what is the bit pattern for the variable i after the execution of line 10 in the above code?

Answer 1

Hello
in the question we find the value of i and then convert it from its hexvalue to the binary bit pattern .After we get the binary bit pattern we just partition the 32 bits of the pattern into 3 segments according to the rules of IEEE 32 bit floating point representation .