hw1_solution.txt

Problem 1
There exist other valid expressions, but these were by far the most common
    A.  K = 17      (x << 4) + x
    B.  K = -7      x - (x << 3)
    C.  K = 60      (x << 6) - (x << 2)
    D.  K = -112    (x << 4) - (x << 7)

Problem 2
    A.  (float) x == (float) dx             True, rounding will be the same
    B.  dx - dy == (double)(x - y)          False, under/overflow with int substraction
    C.  (dx + dy) + dz == dx + (dy + dz)    True, associativity held because values stay within double's range of perfect precision
    D.  (dx * dy) * dz == dx * (dy * dz)    False, associativity not held because values can exceed double's range of perfect precision
    E.  dx / dx == dz / dz                  False, divide by zero

Problem 3
Many answers suggested precision differences between float and double. This was not what we were going for, but was a subset of the correct answer:
    You should not attempt to compare floating-point values with == at all because of possible losses in accuracy due to limited precision during calculations. If you must, use some form of epsilon comparison: |f1 - f2| < e

Problem 4
    M       1.875
    E       3
    frac    0b1110000....... ("111" or ".111" were accepted with full points)

Problem 5
    A.  Symbol names (IE. function names)
    B.  SHL and SAL for left-shift, SHR and SAR for right-shift. SH means logical shift, SA means arithmetic shift
    C.  You had to note something interesting you discovered to get full points
    D.  The symbols have been stripped from the files. This can be replicated using gcc's "-s" flag