61 lines
1.1 KiB
Markdown
61 lines
1.1 KiB
Markdown
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# Bits, Bytes, and Integers
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## Integers
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### Representation
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### Conversion
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**Mapping Between `signed` and `unsigned`**
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Maintain bit pattern
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so the conversion of negative value of the signed or value over the T_MAX results different interpreted value.
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### Expanding, Truncating
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**expanding of $w$-bit signed integer**
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$X = x_{w-1}x_{w-2}\cdots x_0$
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where $s = x_{w-1}$
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expanding it to $w+k$-bit signed int:
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$X = s_{k}s_{k-1} \cdots s_1 x_{w-1}\cdots x_0,\quad \text{where}\, s_i = s$
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**truncation of $w$-bit signed integer**
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first $k$ bit change
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## C Puzzle
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```c
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int x = foo();
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int y = bar();
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unsigned ux = x;
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unsigned uy = y;
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```
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* `x < 0` -> `((x*2) < 0)`
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* `false`: underflow
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* `ux >= 0`
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* it's converted to `ux >= 0u` so `true` for all ux
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* `x & 7 == 7` -> `(x << 30) < 0`
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* `true`
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* `ux > -1`
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* `always false`, `-1 = uint_max`
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* `x > y` -> `-x < -y`
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* `false`
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* `x * x >= 0`
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* `false`
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* `x > 0 && y > 0` -> `x + y > 0`
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* `x >= 0` -> `-x <= 0`
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* `x <= 0` -> `-x >= 0`
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* `(x|-x) >> 31 == -1`
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* `ux >> 3 == ux/8`
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* `x >> 3 == x/8`
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* `x & (x-1) != 0`
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* `true` |