Floating point IEEE guarantees

I would like to know, for the following cases, if the IEEE standard guarantees every possible case (excluding NaN and infinities) using any cpu adhering to the standard:

• Commutativity: x # y = y # x
• Associativity: (x # y) # z = x # (y # z)
• x - x = 0 (does x - x == 0.0f always return true?)
• x * 0 = 0 (does x * 0.0f == 0.0f always return true?)
• x * 1 = x (does x * 1.0f == x always return true?)
• x / x = 1.0f (does x / x == 1.0f always return true? Except for x = 0 of course)

(# means all operations: + - * /)

1. Commutativity: + and * are guaranteed unless either argument is NaN. - and / are not commutative and division by 0.0 gives you +Inf, -Inf, or NaN according to the numerator. Here I'm not giving any consideration to signed zeros.

2. Associativity. Absolutely not. The addition of two small numbers followed by a large number is a counter-example.

3. x - x is 0 unless x is NaN, +Inf, or -Inf in which case it is NaN.

4. x * 0 is 0 unless x is NaN, +Inf, or -Inf in which case it is NaN.

5. x * 1 is x unless x is NaN in which case it is NaN.

6. x / x is 1 unless x is 0.0, +Inf, -Inf, or NaN in which case it is NaN.

Note the subtle difference of (5).