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sav08:bitwidth_analysis [2008/05/20 18:56] vkuncak |
sav08:bitwidth_analysis [2015/04/21 17:30] (current) |
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| Given a language with signed 64 bit integers, determine as small as possible set of bits needed to store values of variables. | Given a language with signed 64 bit integers, determine as small as possible set of bits needed to store values of variables. | ||
| * e.g. if analysis derives that a subset of $\{0,1,2,\ldots,7\}$ is sufficient, then we can use //byte// type to store the value | * e.g. if analysis derives that a subset of $\{0,1,2,\ldots,7\}$ is sufficient, then we can use //byte// type to store the value | ||
| - | * the analysis becomes even more important if we generate hardware from C code (saving wires) | + | * instead of having multiple integer types, we can have analysis infer the right 'subtypes' (ranges) |
| + | * the analysis becomes even more important if we generate hardware from C code: analysis would enable us to save circuits and power | ||
| Let B = {-32,-31,...,-1,0,1,...,31} be a set of bits. | Let B = {-32,-31,...,-1,0,1,...,31} be a set of bits. | ||
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| One simple rule: $g(x)=$ | One simple rule: $g(x)=$ | ||
| ++++| | ++++| | ||
| - | \[\begin{array}{l} | + | \begin{equation*}\begin{array}{l} |
| let\ L = \min(g(y)) + \min(g(z))-1 \\ | let\ L = \min(g(y)) + \min(g(z))-1 \\ | ||
| let\ U = \max(g(y)) + \max(g(z))+1 \\ | let\ U = \max(g(y)) + \max(g(z))+1 \\ | ||
| Line 22: | Line 23: | ||
| else\ [L,U] | else\ [L,U] | ||
| \end{array} | \end{array} | ||
| - | \] | + | \end{equation*} |
| ++++ | ++++ | ||
| + | |||
| + | Is this the most precise rule possible? ++|No, consider adding only even numbers.++ | ||
| ===== References ===== | ===== References ===== | ||