IEEE-754 binary32 operations are performed with round-to-nearest, ties-to-even, and…

IEEE-754 binary32 operations are performed with round-to-nearest, ties-to-even, and with traps disabled. For each operation below, list every flag among \(\{\text{invalid},\text{ overflow},\text{ underflow},\text{ divide-by-zero},\text{ inexact}\}\) that the default exception handling must raise, and give the default result as a \(32\)-bit encoding. Use the after-rounding definition of underflow: underflow is raised if and only if the computed result is tiny (subnormal or zero) and inexact. Use the canonical quiet NaN \(0\ 11111111\ 10000000000000000000000\) when a quiet NaN is the default result. (a) \((+\infty)+(-\infty)\), where \(+\infty\) is \(0\ 11111111\ 00000000000000000000000\) and \(-\infty\) is \(1\ 11111111\ 00000000000000000000000\). (b) \(M+M\), where \(M\) is the largest finite binary32 value \(0\ 11111110\ 11111111111111111111111\). (c) \(P\times Q\), where \(P\) is the smallest positive normal \(0\ 00000001\ 00000000000000000000000\) and \(Q\) is \(2^{-24}\) encoded as \(0\ 01100111\ 00000000000000000000000\). (d) \(1.0\div(+0)\), where \(1.0\) is \(0\ 01111111\ 00000000000000000000000\) and \(+0\) is \(0\ 00000000\ 00000000000000000000000\). (e) \((+0)\div(+0)\), with \(+0\) as in (d).

Match each case to a standard default-exception rule: invalid \(\infty-\infty\) or \(0/0\); overflow of a huge finite; underflow of a tiny inexact; divide-by-zero of a nonzero finite by zero.