Left shift operations (`<<`) drop the `k` most significant bits and fills the right end of the result with `k` zeros. Right shift operations (`>>`) are classified in two ways:
* **Logical**
* Drops the `k` least significant bits and fills the left end of the result with `k` zeros.
* This mode is always used when calling `>>` on unsigned data.
* Sometimes denoted as `>>>` to disambiguate from arithmetic right shifts.
* **Arithmetic**
* Drops the `k` least significant bits and fills the left end of the result with `k` copies of the most significant bit.
* This mode is usually used when calling `>>` on signed data.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
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Basic
What kinds of left shift operations are there?
Back: Just logical.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
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Basic
What kinds of right shift operations are there?
Back: Logical and arithmetic
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
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Basic
What kind of right shift operation is *usually* applied to signed numbers?
Back: Arithmetic.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
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Basic
What kind of right shift operation is applied to unsigned numbers?
Back: Logical.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
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Basic
What portability issue do shift operations introduce?
Back: There is no standard on whether right shifts of signed numbers are logical or arithmetic.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
In C, it is undefined behavior to shift by more than the width $w$ of an integral type. Typically though, only the last $w$ bits are considered in the computation. For example, given `int32_t x`, `(x << 32) = (x << 0)`.
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Basic
Ignoring UB, what *typically* happens when shifting an `int32_t` by `k ≥ 32` bits?
Back: The shift value is interpreted as `k mod 32`.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
* Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
* Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik, *Concrete Mathematics: A Foundation for Computer Science*, 2nd ed (Reading, Mass: Addison-Wesley, 1994).
