Power-of-2 Boundaries

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Sections

• 3-1 Rounding Up/Down to a Multiple of a Known Power of 2
• 3-2 Rounding Up/Down to the Next Power of 2
• 3-3 Detecting a Power-of-2 Boundary Crossing

Problems

1. Show how to round an unsigned integer to the nearest multiple of 8, with the halfway case (a) rounding up, (b) rounding down, and (c) rounding up or down, whichever makes the next bit to the left a zero, unbiased rounding.

2. Show how to round an unsigned integer to the nearest multiple of 10, with the halfway case (a) rounding up, (b) rounding down, and (c) rounding up or down, whichever results in an even multiple of 10. Feel free to use division, remaindering, and multiplication instructions, and do not be concerned about values very close to the largest unsigned integer.

3. Code a function in C that does an unaligned load. The function is given an address $a$, and it loads the four bytes from addresses $a$ through $a+3$ into a 32-bit GPR, as if those four bytes contained an integer. Parameter $a$ addresses the low-order byte, that is, the machine is little-endian. The function should be branch free, it should execute at most two load instructions and, if $a$ is fullword aligned, it must not attempt to load from address $a+4$, because that may be in a read-protected block.