Graph transformations and C bit-fields.
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@ -350,7 +350,7 @@
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@ -413,7 +413,7 @@
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"encoding/floating-point.md": "d19e3f992bf2e073d2049fb0973c89bd",
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"set/directed-graph.md": "b4b8ad1be634a0a808af125fe8577a53",
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"_journal/2024-10-01.md": "2547ea281e11e2bc728d2b21787f1270",
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"c17/alignment.md": "bda6444de141aeb8072d3ef2971c4d30",
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"_journal/2024-11-05.md": "6a599e6bc9dcd12a0940956285ae4d00",
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"_journal/2024-11/2024-11-05.md": "79a1304037e18fefa135d576db040784",
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"_journal/2024-11/2024-11-07.md": "434ec3f15d7065ea740127aa8477dd17",
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"x86-64/directives.md": "019c1c1d04efb26c3e8758aac4543cc7",
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"geometry/cartesian.md": "1977d6fd05109456cf1824822b836b02",
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"geometry/cartesian.md": "71dd4816e1ead4db46b8189e7d275f34",
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"_journal/2024-11/2024-11-09.md": "46f3a640223ef533f4523837b67b57c3",
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@ -966,7 +966,7 @@
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"_journal/2024-11/2024-11-21.md": "951b6034d60a40dbd8201c50abf0dbb9",
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"_journal/2024-11/2024-11-20.md": "951b6034d60a40dbd8201c50abf0dbb9",
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"_journal/2024-11/2024-11-19.md": "d879f57154cb27cb168eb1f1f430e312",
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"set/cardinality.md": "b396048272652dcf49c875e723377ff4",
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"geometry/area.md": "7f947bb5ac782495a1fb4a63bb2463e7",
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"_journal/2024-11-23.md": "911f82ab8aede5ecdb96493aef64b0b9",
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"_journal/2024-11/2024-11-22.md": "51117030e2364dbce3a8d507dead86ae",
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"_journal/2024-12/2024-12-04.md": "965f6619edf1002d960203e3e12a413b",
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"_journal/2024-12-06.md": "d75323d0fec57f4fc1f13cb4370df18d",
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"_journal/2024-12/2024-12-05.md": "4f3b1e7a43e01cc97b0eed6fbc6c1f96",
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"calculus/integrals.md": "a7ef5031ca474cd9d37c1aea85e96237",
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"calculus/integrals.md": "e8d36a8fae9cd785374f419996ef5269",
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"_journal/2024-12-07.md": "bfb6c4db0acbacba19f03a04ec29fa5c",
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"_journal/2024-12-08.md": "5662897539b222db1af45dcd217f0796",
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"_journal/2024-12/2024-12-11.md": "e7393c01b44c5b804f86f45b8b899b59",
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"encoding/uri.md": "394abe477b882e1414dd2fb151fea823",
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"encoding/xml.md": "5b345c09ac60821f88ed5b592e411df6",
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"linkers/elf.md": "83a27a7d71ca26f8f034770a31d58fa0",
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},
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"fields_dict": {
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"Basic": [
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---
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title: "2024-12-19"
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---
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- [x] Anki Flashcards
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- [x] KoL
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- [x] OGS
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- [ ] Sheet Music (10 min.)
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- [ ] Korean (Read 1 Story)
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* Additional flashcards on scaling and shifting.
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* Notes on C [[alignment#Bit-Fields|bit-fields]].
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title: "2024-12-16"
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---
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- [ ] Anki Flashcards
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- [x] Anki Flashcards
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- [x] KoL
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- [ ] OGS
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- [ ] Sheet Music (10 min.)
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- [ ] Korean (Read 1 Story)
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* Notes on sections found within an [[elf|ELF]] file.
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* Additional examples on cardinal numbers and their relation to the recursion theorem.
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* Additional examples on cardinal numbers and their relation to the recursion theorem.
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* Reification in the context of RDF.
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---
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title: "2024-12-17"
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---
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- [x] Anki Flashcards
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- [x] KoL
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- [x] OGS
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- [ ] Sheet Music (10 min.)
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- [ ] Korean (Read 1 Story)
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* More notes on [[elf#Relocatable Object Files|relocatable object files]].
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@ -0,0 +1,11 @@
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---
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title: "2024-12-18"
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---
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- [x] Anki Flashcards
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- [x] KoL
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- [x] OGS
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- [ ] Sheet Music (10 min.)
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- [ ] Korean (Read 1 Story)
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* Identities regarding cardinal numbers.
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@ -468,7 +468,482 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
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<!--ID: 1731165663242-->
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END%%
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## Bit-Fields
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A member of a structure or union may be declared to consist of a specified number of bits (including a sign bit, if any). Such a member is called a **bit-field**; its width is preceded by a colon. Its width must be an ICE with a nonnegative value that does not exceed the width of an object of the type that would be specified were the colon and expression omitted.
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A bit-field shall have a type is a qualified or unqualified version of `_Bool`, `signed int`, `unsigned int`, or some other implementation-defined type.
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%%ANKI
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Basic
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A bit-field can be declared as members of what?
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Back: `struct`s or `union`s.
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Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
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<!--ID: 1734662614053-->
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END%%
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%%ANKI
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Basic
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How is a bit-field declared?
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Back: As a member of a `struct` or `union` with width preceded by a colon.
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Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
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<!--ID: 1734662614057-->
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END%%
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%%ANKI
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Basic
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What *kind* of expression must the width of a bit-field be?
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Back: An ICE.
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Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
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<!--ID: 1734662614060-->
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END%%
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%%ANKI
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Basic
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What non-implementation-defined types can a bit-field be declared with?
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Back: `_Bool`, `signed int`, or `unsigned int`.
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Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
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<!--ID: 1734662614063-->
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END%%
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%%ANKI
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Basic
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What types can a bit-field be declared with?
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Back: `_Bool`, `signed int`, `unsigned int`, or some other implementation-defined type.
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Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
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<!--ID: 1734662614068-->
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END%%
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%%ANKI
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Basic
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What is the sign of the following bit-field?
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```c
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struct foo { int bar : 1; };
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```
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Back: N/A. This is implementation-defined.
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Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
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<!--ID: 1734662614071-->
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END%%
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%%ANKI
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Basic
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What is the sign of the following bit-field?
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```c
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struct foo { signed bar : 1; };
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```
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Back: Signed.
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Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
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<!--ID: 1734662614075-->
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END%%
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%%ANKI
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Basic
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What is the sign of the following bit-field?
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```c
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struct foo { unsigned bar : 1; };
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```
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Back: Unsigned.
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Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
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<!--ID: 1734662614079-->
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END%%
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%%ANKI
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Basic
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Which unary operator cannot be applied to a bit-field object?
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Back: `&`
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Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
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<!--ID: 1734662614084-->
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END%%
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%%ANKI
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Basic
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What compilation error exists in the following translation unit?
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```c
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#include <stdio.h>
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struct foo { int a; int b : 4; };
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int main(void) {
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struct foo bar = { .a = 1, .b = 1 };
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printf("%p\n", (void *)&bar.b);
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}
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```
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Back: Cannot take the address-of a bit-field.
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Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
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<!--ID: 1734662614089-->
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END%%
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%%ANKI
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Basic
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What compilation error exists in the following translation unit?
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```c
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#include <stdio.h>
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struct foo { int a; int b : 4; };
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int main(void) {
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struct foo bar = { .a = 1, .b = 1 };
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printf("%p\n", (void *)&bar.a);
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}
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```
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Back: N/A. This compiles correctly.
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Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
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<!--ID: 1734662614094-->
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END%%
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%%ANKI
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Basic
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What is an unnamed bit-field?
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Back: A bit-field with no declarator.
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Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
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<!--ID: 1734662614099-->
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END%%
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### Packing
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An implementation may allocate any addressable storage unit large enough to hold a bit-field. If enough space remains, a bit-field that immediately follows another in a structure shall be packed into adjacent bits of the same unit.
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If insufficient space remains, whether a bit-field that does not fit is put into the next unit or overlaps adjacent units is implementation-defined.
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A bit-field structure member with a width of `0` indicates that no further bit-field is to be packed into the unit in which the previous bit-field, if any, was placed.
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%%ANKI
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Basic
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What are the addressable storage units supported in x86-64?
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Back: A byte, word, double word, or quad word.
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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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Tags: x86-64
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<!--ID: 1734662614105-->
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END%%
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%%ANKI
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Basic
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What does the C standard mean by an "addressable storage unit"?
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Back: A memory unit that can be directly addressed/manipulated by the processor.
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Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
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<!--ID: 1734662614110-->
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END%%
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%%ANKI
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Basic
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Does x86-64 allow bit-fields to overlap adjacent addressable storage units?
|
||||
Back: No.
|
||||
Reference: Raymond, Eric. “The Lost Art of Structure Packing.” Accessed November 4, 2024. [http://www.catb.org/esr/structure-packing/](http://www.catb.org/esr/structure-packing/).
|
||||
Tags: x86-64
|
||||
<!--ID: 1734662614115-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What does a bit-field of width `0` indicate?
|
||||
Back: No subsequent bit-field can be packed into the unit in which the previous bit-field, if any, was placed.
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
<!--ID: 1734662614122-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What is wrong with the following `struct` definition?
|
||||
```c
|
||||
struct foo { unsigned bar : 0; };
|
||||
```
|
||||
Back: A bit-field of width `0` cannot have a declarator.
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
<!--ID: 1734662614129-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
How is the following `struct` correctly written?
|
||||
```c
|
||||
struct foo { unsigned bar : 0; };
|
||||
```
|
||||
Back:
|
||||
```c
|
||||
struct foo { unsigned : 0; };
|
||||
```
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
<!--ID: 1734662614138-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Assume a `4`-byte `unsigned int`. What is wrong with the following `struct` definition?
|
||||
```c
|
||||
struct foo { unsigned bar : 31; };
|
||||
```
|
||||
Back: N/A. This is correct.
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
Tags: x86-64
|
||||
<!--ID: 1734662614146-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Assume a `4`-byte `unsigned int`. What is wrong with the following `struct` definition?
|
||||
```c
|
||||
struct foo { unsigned bar : 32; };
|
||||
```
|
||||
Back: N/A. This is correct.
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
Tags: x86-64
|
||||
<!--ID: 1734662614152-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Assume a `4`-byte `unsigned int`. What is wrong with the following `struct` definition?
|
||||
```c
|
||||
struct foo { unsigned bar : 33; };
|
||||
```
|
||||
Back: The width of a bit-field cannot exceed its types (in this case `unsigned int`).
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
Tags: x86-64
|
||||
<!--ID: 1734662614158-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Assume a byte-sized storage unit, no overlapping units, and low-to-high order. How is the following packed in memory?
|
||||
```c
|
||||
struct foo {
|
||||
signed a : 4;
|
||||
signed b : 2;
|
||||
signed c : 4;
|
||||
};
|
||||
```
|
||||
Back:
|
||||
```c
|
||||
struct foo {
|
||||
_padding : 2; // 2 bits
|
||||
signed b : 2; // 2 bits
|
||||
signed a : 4; // 4 bits
|
||||
_padding : 4; // 4 bits
|
||||
signed c : 4; // 4 bits
|
||||
};
|
||||
```
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
<!--ID: 1734662614163-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Assume a byte-sized storage unit, overlapping units, and low-to-high order. How is the following packed in memory?
|
||||
```c
|
||||
struct foo {
|
||||
signed a : 4;
|
||||
signed : 0;
|
||||
signed c : 4;
|
||||
};
|
||||
```
|
||||
Back:
|
||||
```c
|
||||
struct foo {
|
||||
_padding : 4; // 4 bits
|
||||
signed a : 4; // 4 bits
|
||||
_padding : 4; // 4 bits
|
||||
signed c : 4; // 4 bits
|
||||
};
|
||||
```
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
<!--ID: 1734664080915-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Assume a byte-sized storage unit, overlapping units, and high-to-low order. How is the following packed in memory?
|
||||
```c
|
||||
struct foo {
|
||||
signed a : 4;
|
||||
signed : 0;
|
||||
signed c : 4;
|
||||
};
|
||||
```
|
||||
Back:
|
||||
```c
|
||||
struct foo {
|
||||
signed a : 4; // 4 bits
|
||||
_padding : 4; // 4 bits
|
||||
signed c : 4; // 4 bits
|
||||
_padding : 4; // 4 bits
|
||||
};
|
||||
```
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
<!--ID: 1734664080919-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Assume a `32`-bit storage unit, no overlapping units, and low-to-high order. How is the following packed in memory?
|
||||
```c
|
||||
struct foo {
|
||||
signed a : 4;
|
||||
signed b : 2;
|
||||
signed c : 4;
|
||||
};
|
||||
```
|
||||
Back:
|
||||
```c
|
||||
struct foo {
|
||||
_padding : 22; // 22 bits
|
||||
signed c : 4; // 4 bits
|
||||
signed b : 2; // 2 bits
|
||||
signed a : 4; // 4 bits
|
||||
};
|
||||
```
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
<!--ID: 1734662614168-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Assume a byte-sized storage unit, overlapping units, and low-to-high order. How is the following packed in memory?
|
||||
```c
|
||||
struct foo {
|
||||
signed a : 4;
|
||||
signed b : 2;
|
||||
signed c : 4;
|
||||
};
|
||||
```
|
||||
Back:
|
||||
```c
|
||||
struct foo {
|
||||
_padding : 6; // 6 bits
|
||||
signed c : 4; // 4 bits
|
||||
signed b : 2; // 2 bits
|
||||
signed a : 4; // 4 bits
|
||||
};
|
||||
```
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
<!--ID: 1734662614174-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Assume a `32`-bit storage unit, no overlapping units, and low-to-high order. How is the following packed in memory?
|
||||
```c
|
||||
struct foo {
|
||||
signed a : 4;
|
||||
signed : 0;
|
||||
signed c : 4;
|
||||
};
|
||||
```
|
||||
Back:
|
||||
```c
|
||||
struct foo {
|
||||
_padding : 28; // 28 bits
|
||||
signed c : 4; // 4 bits
|
||||
_padding : 28; // 28 bits
|
||||
signed a : 4; // 4 bits
|
||||
};
|
||||
```
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
<!--ID: 1734664080924-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Assume a byte-sized storage unit, overlapping units, and high-to-low order. How is the following packed in memory?
|
||||
```c
|
||||
struct foo {
|
||||
signed a : 4;
|
||||
signed b : 2;
|
||||
signed c : 4;
|
||||
};
|
||||
```
|
||||
Back:
|
||||
```c
|
||||
struct foo {
|
||||
signed a : 4; // 4 bits
|
||||
signed b : 2; // 2 bits
|
||||
signed c : 4; // 4 bits
|
||||
_padding : 6; // 6 bits
|
||||
};
|
||||
```
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
<!--ID: 1734662614181-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Assume a byte-sized storage unit, no overlapping units, and high-to-low order. How is the following packed in memory?
|
||||
```c
|
||||
struct foo {
|
||||
signed a : 4;
|
||||
signed b : 2;
|
||||
signed c : 4;
|
||||
};
|
||||
```
|
||||
Back:
|
||||
```c
|
||||
struct foo {
|
||||
signed a : 4; // 4 bits
|
||||
signed b : 2; // 2 bits
|
||||
_padding : 2; // 2 bits
|
||||
signed c : 4; // 4 bits
|
||||
_padding : 4; // 4 bits
|
||||
};
|
||||
```
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
<!--ID: 1734662614188-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Assume a `32`-bit storage unit, overlapping units, and high-to-low order. How is the following packed in memory?
|
||||
```c
|
||||
struct foo {
|
||||
signed a : 4;
|
||||
signed b : 2;
|
||||
signed c : 4;
|
||||
};
|
||||
```
|
||||
Back:
|
||||
```c
|
||||
struct foo {
|
||||
signed a : 4; // 4 bits
|
||||
signed b : 2; // 2 bits
|
||||
signed c : 4; // 4 bits
|
||||
_padding : 22; // 22 bits
|
||||
};
|
||||
```
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
<!--ID: 1734662614195-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What implementation-defined property guarantees tightly-packed bit-fields?
|
||||
Back: Whether bit-fields can overlap adjacent addressable storage units.
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
<!--ID: 1734662614202-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Cloze
|
||||
An implementation may allocate any {addressable storage} unit large enough to hold a bit-field.
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
<!--ID: 1734662614208-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What does it mean for bit-fields to be allocated low-to-high?
|
||||
Back: They are packed starting from the least significant bit of the addressable storage unit.
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
<!--ID: 1734664080929-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What does it mean for bit-fields to be allocated high-to-low?
|
||||
Back: They are packed starting from the most significant bit of the addressable storage unit.
|
||||
Reference: “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
<!--ID: 1734664080934-->
|
||||
END%%
|
||||
|
||||
## Bibliography
|
||||
|
||||
* Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
* “ISO: Programming Languages - C17,” April 2017, [https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf](https://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf).
|
||||
* Raymond, Eric. “The Lost Art of Structure Packing.” Accessed November 4, 2024. [http://www.catb.org/esr/structure-packing/](http://www.catb.org/esr/structure-packing/).
|
||||
|
|
@ -645,7 +645,7 @@ END%%
|
|||
|
||||
%%ANKI
|
||||
Basic
|
||||
Which component of a compiler driver produces ASCII relocatable object files?
|
||||
Which component of a compiler driver produces relocatable object files?
|
||||
Back: The assembler.
|
||||
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
<!--ID: 1733607099587-->
|
||||
|
|
@ -655,7 +655,7 @@ The operating system provides a function called the **loader** that copies the c
|
|||
|
||||
%%ANKI
|
||||
Basic
|
||||
What function does the OS provider to run an executable object file?
|
||||
What function does the OS provide to run executable object files?
|
||||
Back: The loader.
|
||||
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
<!--ID: 1733607099593-->
|
||||
|
|
|
|||
|
|
@ -7,7 +7,7 @@ tags:
|
|||
- integral
|
||||
---
|
||||
|
||||
## Overview
|
||||
## Step Functions
|
||||
|
||||
Let $s$ be a step function defined on [[intervals|interval]] $[a, b]$, and let $P = \{x_0, x_1, \ldots, x_n\}$ be a [[intervals#Partitions|partition]] of $[a, b]$ such that $s$ is constant on the open subintervals of $P$. Denote by $s_k$ the constant value that $s$ takes in the $k$th open subinterval, so that $$s(x) = s_k \quad\text{if}\quad x_{k-1} < x < x_k, \quad k = 1, 2, \ldots, n.$$
|
||||
|
||||
|
|
|
|||
|
|
@ -1,6 +1,6 @@
|
|||
---
|
||||
title: Binary
|
||||
TARGET DECK: Obsidian::H&SS
|
||||
TARGET DECK: Obsidian::STEM
|
||||
FILE TAGS: binary
|
||||
tags:
|
||||
- binary
|
||||
|
|
@ -176,6 +176,42 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
|
|||
<!--ID: 1707661283782-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Cloze
|
||||
A big-endian system stores the {most} significant byte at the {smallest} memory address.
|
||||
Reference: “Endianness,” in _Wikipedia_, December 19, 2024, [https://en.wikipedia.org/w/index.php?title=Endianness](https://en.wikipedia.org/w/index.php?title=Endianness&oldid=1264018894).
|
||||
<!--ID: 1734664080894-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Cloze
|
||||
A big-endian system stores the {least} significant byte at the {largest} memory address.
|
||||
Reference: “Endianness,” in _Wikipedia_, December 19, 2024, [https://en.wikipedia.org/w/index.php?title=Endianness](https://en.wikipedia.org/w/index.php?title=Endianness&oldid=1264018894).
|
||||
<!--ID: 1734664080900-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Cloze
|
||||
A little-endian system stores the {least} significant byte at the {smallest} memory address.
|
||||
Reference: “Endianness,” in _Wikipedia_, December 19, 2024, [https://en.wikipedia.org/w/index.php?title=Endianness](https://en.wikipedia.org/w/index.php?title=Endianness&oldid=1264018894).
|
||||
<!--ID: 1734664080903-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Cloze
|
||||
A little-endian system stores the {most} significant byte at the {largest} memory address.
|
||||
Reference: “Endianness,” in _Wikipedia_, December 19, 2024, [https://en.wikipedia.org/w/index.php?title=Endianness](https://en.wikipedia.org/w/index.php?title=Endianness&oldid=1264018894).
|
||||
<!--ID: 1734664080907-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Which of little- or big-endian more closely mirrors the way numbers are written in English?
|
||||
Back: Big-endian.
|
||||
Reference: “Endianness,” in _Wikipedia_, December 19, 2024, [https://en.wikipedia.org/w/index.php?title=Endianness](https://en.wikipedia.org/w/index.php?title=Endianness&oldid=1264018894).
|
||||
<!--ID: 1734664080911-->
|
||||
END%%
|
||||
|
||||
```c
|
||||
#include <stdint.h>
|
||||
#include <stdio.h>
|
||||
|
|
@ -192,4 +228,5 @@ The above snippet can be used to check endianness on the current machine. If big
|
|||
|
||||
## Bibliography
|
||||
|
||||
* 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.
|
||||
* “Endianness,” in _Wikipedia_, December 19, 2024, [https://en.wikipedia.org/w/index.php?title=Endianness](https://en.wikipedia.org/w/index.php?title=Endianness&oldid=1264018894).
|
||||
|
|
@ -442,7 +442,7 @@ END%%
|
|||
|
||||
%%ANKI
|
||||
Cloze
|
||||
The exponent field of a `float` has {`8`} bits and a `double` has {`11`} bits.
|
||||
The exponent field of a `float` has {`8`} bits whereas a `double` has {`11`} bits.
|
||||
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
Tags: c17
|
||||
<!--ID: 1710556915030-->
|
||||
|
|
|
|||
|
|
@ -128,6 +128,114 @@ Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web
|
|||
<!--ID: 1722191359882-->
|
||||
END%%
|
||||
|
||||
## Reification
|
||||
|
||||
**Reification** refers to the process by which an abstract idea is made concrete. In the context of RDF, it refers to writing RDF statements about RDF statements.
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What is reification?
|
||||
Back: The process by which an abstract idea is made concrete.
|
||||
Reference: “Reification (Knowledge Representation),” in _Wikipedia_, October 3, 2023, [https://en.wikipedia.org/w/index.php?title=Reification_(knowledge_representation)](https://en.wikipedia.org/w/index.php?title=Reification_(knowledge_representation)&oldid=1178437461).
|
||||
<!--ID: 1734385502410-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
In the context of RDF, what does reification typically refer to?
|
||||
Back: Creating RDF statements about RDF statements.
|
||||
Reference: “Reification (Knowledge Representation),” in _Wikipedia_, October 3, 2023, [https://en.wikipedia.org/w/index.php?title=Reification_(knowledge_representation)](https://en.wikipedia.org/w/index.php?title=Reification_(knowledge_representation)&oldid=1178437461).
|
||||
<!--ID: 1734385502419-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
In the context of RDF, what abstract notion is typically reified?
|
||||
Back: RDF statements.
|
||||
Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
|
||||
<!--ID: 1734385502422-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What term describes making an abstract concept concrete?
|
||||
Back: Reification.
|
||||
Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
|
||||
<!--ID: 1734385502427-->
|
||||
END%%
|
||||
|
||||
This kind of metadata about statements often take the forms of:
|
||||
|
||||
* **Provenance**. Information about the source of a statement.
|
||||
* **Likelihood**. Information quantifying some probability regarding the statement.
|
||||
* **Context**. Information about a setting in which a statement holds.
|
||||
* **Time frame**. Information that holds within a particular period of time.
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What might reifying a statement with respect to its provenance refer to?
|
||||
Back: Information about the source of the statement.
|
||||
Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
|
||||
<!--ID: 1734385502431-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What "form" of reification does the following sentence take on? $$\text{Wikipedia says Shakespeare wrote Hamlet.}$$
|
||||
Back: Provenance.
|
||||
Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
|
||||
<!--ID: 1734385502435-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What might reifying a statement with respect to its likelihood refer to?
|
||||
Back: Information quantifying some probability of the statement holding.
|
||||
Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
|
||||
<!--ID: 1734385502439-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What "form" of reification does the following sentence take on? $$\text{It is 90\% probable that Shakespeare wrote Hamlet.}$$
|
||||
Back: Likelihood.
|
||||
Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
|
||||
<!--ID: 1734385502443-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What might reifying a statement with respect to its context refer to?
|
||||
Back: Information about a setting in which the statement holds.
|
||||
Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
|
||||
<!--ID: 1734385502448-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What "form" of reification does the following sentence take on? $$\text{Kenneth Branagh played Hamlet in the movie.}$$
|
||||
Back: Context.
|
||||
Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
|
||||
<!--ID: 1734385502453-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What might reifying a statement with respect to its time frame refer to?
|
||||
Back: Information about a period of time in which the statement holds.
|
||||
Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
|
||||
<!--ID: 1734385502458-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What "form" of reification does the following sentence take on? $$\text{Hamlet plays on Broadway Jan. 11th through Mar. 12th.}$$
|
||||
Back: Time frame.
|
||||
Reference: Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
|
||||
<!--ID: 1734385502463-->
|
||||
END%%
|
||||
|
||||
## Bibliography
|
||||
|
||||
* Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
|
||||
* Allemang, Dean, James A. Hendler, and Fabien L. Gandon. _Semantic Web for the Working Ontologist_. 3e ed. ACM Books 33. New York: Association for computing machinery, 2020.
|
||||
* “Reification (Knowledge Representation),” in _Wikipedia_, October 3, 2023, [https://en.wikipedia.org/w/index.php?title=Reification_(knowledge_representation)](https://en.wikipedia.org/w/index.php?title=Reification_(knowledge_representation)&oldid=1178437461).
|
||||
|
|
@ -131,13 +131,13 @@ Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Int
|
|||
<!--ID: 1731185808252-->
|
||||
END%%
|
||||
|
||||
## Translations
|
||||
## Transformations
|
||||
|
||||
There are two kinds of translations that we can do to a graph: **shifting** and **scaling**. A **reflection** is a special case of scaling.
|
||||
There are two kinds of transformations that we can do to a graph: **shifting** and **scaling**. A **reflection** is a special case of scaling.
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What are the two kinds of translations that can be done to a graph?
|
||||
What are the two kinds of transformations that can be done to a graph?
|
||||
Back: Shifting and scaling.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1733520214987-->
|
||||
|
|
@ -145,7 +145,7 @@ END%%
|
|||
|
||||
%%ANKI
|
||||
Basic
|
||||
Which of the two kinds of translations is reflection a special case of?
|
||||
Which of the two kinds of transformations is reflection a special case of?
|
||||
Back: Scaling.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1733520269110-->
|
||||
|
|
@ -165,6 +165,150 @@ Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” acces
|
|||
<!--ID: 1733522558480-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Given function $f$, which of $a$, $b$, $c$, and/or $d$ relate to shifting? $$y = af(b[x - c]) + d$$
|
||||
Back: $c$ and $d$
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734620943896-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Given function $f$, which of $a$, $b$, $c$, and/or $d$ relate to a horizontal transformation? $$y = af(b[x - c]) + d$$
|
||||
Back: $b$ and $c$
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734620943904-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Given function $f$, which of $a$, $b$, $c$, and/or $d$ relate to a vertical transformation? $$y = af(b[x - c]) + d$$
|
||||
Back: $a$ and $d$.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734620943910-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Given function $f$, which of $a$, $b$, $c$, and/or $d$ relate to scaling? $$y = af(b[x - c]) + d$$
|
||||
Back: $a$ and $b$.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734620943916-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Given function $f$, which of $a$, $b$, $c$, and/or $d$ apply a transformation that "acts normally"? $$y = af(b[x - c]) + d$$
|
||||
Back: $a$ and $d$.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734620943921-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Given function $f$, which of $a$, $b$, $c$, and/or $d$ apply a transformation that "acts inversely"? $$y = af(b[x - c]) + d$$
|
||||
Back: $b$ and $c$.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734620943926-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Which of horizontal and/or vertical transformations "act inversely"?
|
||||
Back: Horizontal transformations.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734620943931-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Which of horizontal and/or vertical transformations "act normally"?
|
||||
Back: Vertical transformations.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734620943937-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
How is the graph of $y = f(x)$ transformed in the graph of $y = \frac{1}{2}f(\frac{x}{3})$?
|
||||
Back: It's horizontally scaled by $3$ and vertically compressed by $2$.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656174535-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Consider $y = f(x)$. Is $y = af(bx)$ first scaled vertically or horizontally?
|
||||
Back: N/A. There is no order of operations in this case.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656174588-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
How is the graph of $y = f(x)$ transformed in the graph of $y = f(x - 3) + 2$?
|
||||
Back: It's shifted right by $3$ and shifted up by $2$.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656174596-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Consider $y = f(x)$. Is $y = f(x + a) + b$ first shifted vertically or horizontally?
|
||||
Back: N/A. There is no order of operations in this case.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656174604-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
How is the graph of $y = f(x)$ transformed in the graph of $y = 2f(x) + 5$?
|
||||
Back: It's vertically scaled by $2$ and then shifted up by $5$.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656174610-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Consider $y = f(x)$. Is $y = af(x) + b$ first scaled or shifted?
|
||||
Back: Scaled.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656174615-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Consider $y = f(x)$. Is $y = f(ax) + b$ first scaled or shifted?
|
||||
Back: Scaled.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656174619-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
How is the graph of $y = f(x)$ transformed in the graph of $y = f(2x - 3)$?
|
||||
Back: It's horizontally compressed by $2$ and then shifted right by $3/2$.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656174624-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose $f(x)$ has domain $(-2, 5)$. What is the domain of $2f(x - 3) - 5$?
|
||||
Back: $(1, 8)$
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734657098882-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose $f(x)$ has range $[4, 8]$. What is the range of $2f(x - 3) - 5$?
|
||||
Back: $[3, 11]$
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734657098887-->
|
||||
END%%
|
||||
|
||||
### Shifting
|
||||
|
||||
A **vertical shift** adds/subtracts a constant to every $y$-coordinate of a graph, leaving the $x$-coordinate unchanged. A **horizontal shift** adds/subtracts a constant to every $x$-coordinate of a graph, leaving the $y$-coordinate unchanged.
|
||||
|
|
@ -179,7 +323,7 @@ END%%
|
|||
|
||||
%%ANKI
|
||||
Basic
|
||||
Which of the two fundamental graph translations is considered "rigid"?
|
||||
Which of the two fundamental graph transformations is considered "rigid"?
|
||||
Back: Shifts.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1733522558483-->
|
||||
|
|
@ -215,7 +359,7 @@ END%%
|
|||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $f(x)$ be a function and $k$ be a constant. What kind of translation is $f(x + k)$?
|
||||
Let $f(x)$ be a function and $k$ be a constant. What kind of transformations is $f(x + k)$?
|
||||
Back: A horizontal shift.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1733520215013-->
|
||||
|
|
@ -223,7 +367,7 @@ END%%
|
|||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $f(x)$ be a function and $k$ be a constant. What kind of translation is $f(x) + k$?
|
||||
Let $f(x)$ be a function and $k$ be a constant. What kind of transformations is $f(x) + k$?
|
||||
Back: A vertical shift.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1733520215016-->
|
||||
|
|
@ -311,6 +455,70 @@ Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” acces
|
|||
<!--ID: 1733520215056-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Horizontal shifting of a function affects which of its range and/or domain?
|
||||
Back: The domain.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938097-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose $f(x)$ has domain $(-2, 5)$. What is the domain of $f(x - 2)$?
|
||||
Back: $(0, 7)$
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938102-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose $f(x)$ has domain $(-2, 5)$. What is the domain of $f(x + 2)$?
|
||||
Back: $(-4, 3)$
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938105-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose $f(x)$ has domain $(-2, 5)$. What is the domain of $f(x) + 2$?
|
||||
Back: $(-2, 5)$
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938109-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Vertical shifting of a function affects which of its range and/or domain?
|
||||
Back: The range.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938112-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose $f(x)$ has range $[4, 8]$. What is the range of $f(x - 2)$?
|
||||
Back: $[4, 8]$
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938116-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose $f(x)$ has range $[4, 8]$. What is the range of $f(x) - 2$?
|
||||
Back: $[2, 6]$
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938120-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose $f(x)$ has range $[4, 8]$. What is the range of $f(x) + 2$?
|
||||
Back: $[6, 10]$
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938124-->
|
||||
END%%
|
||||
|
||||
### Scaling
|
||||
|
||||
A **vertical scaling** will multiply/divide every $y$-coordinate of a graph, leaving the $x$-coordinate unchanged. A **horizontal scaling** will multiply/divide every $x$-coordinate of a graph, leaving the $y$-coordinate unchanged.
|
||||
|
|
@ -341,7 +549,7 @@ END%%
|
|||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $f(x)$ be a function and $k$ be a constant. What kind of translation is $kf(x)$?
|
||||
Let $f(x)$ be a function and $k$ be a constant. What kind of transformation is $kf(x)$?
|
||||
Back: A vertical scaling.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1733522558503-->
|
||||
|
|
@ -349,7 +557,7 @@ END%%
|
|||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $f(x)$ be a function and $k$ be a constant. What kind of translation is $f(kx)$?
|
||||
Let $f(x)$ be a function and $k$ be a constant. What kind of transformation is $f(kx)$?
|
||||
Back: A horizontal scaling.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1733522558507-->
|
||||
|
|
@ -425,6 +633,144 @@ Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” acces
|
|||
<!--ID: 1733522558555-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Horizontal scaling of a function affects which of its range and/or domain?
|
||||
Back: The domain.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938129-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose $f(x)$ has domain $(-2, 5)$. What is the domain of $f(2x)$?
|
||||
Back: $(-1, 5/2)$
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938133-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose $f(x)$ has domain $(-2, 5)$. What is the domain of $2f(x)$?
|
||||
Back: $(-2, 5)$
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938137-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose $f(x)$ has domain $(-2, 5)$. What is the domain of $f(x / 2)$?
|
||||
Back: $(-4, 10)$
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938141-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Vertical scaling of a function affects which of its range and/or domain?
|
||||
Back: The range.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938145-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose $f(x)$ has range $[4, 8]$. What is the range of $f(2x)$?
|
||||
Back: $[4, 8]$
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938149-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose $f(x)$ has range $[4, 8]$. What is the range of $2f(x)$?
|
||||
Back: $[8, 16]$
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938152-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose $f(x)$ has range $[4, 8]$. What is the range of $f(x) / 2$?
|
||||
Back: $[2, 4]$
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938156-->
|
||||
END%%
|
||||
|
||||
### Reflecting
|
||||
|
||||
A **reflection** is a special case of a [[#Scaling|scaling]].
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
A reflection is a special case of what other kind of transformation?
|
||||
Back: A scaling.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734620943942-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Cloze
|
||||
To reflect a function's graph about the {$y$}-axis, multiply its {inputs} by $-1$.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734620943947-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Cloze
|
||||
To reflect a function's graph about the {$x$}-axis, multiply its {outputs} by $-1$.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734620943953-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Consider the graph of $f(x)$. Is $f(-x)$ its horizontal or vertical reflection?
|
||||
Back: Horizontal (reflection along the $y$-axis).
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938160-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose $f(x)$ has domain $(-2, 5)$. What is the domain of $f(-x)$?
|
||||
Back: $(-5, 2)$
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938163-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose $f(x)$ has domain $(-2, 5)$. What is the range of $f(-x)$?
|
||||
Back: The same as that of $f(x)$.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938167-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Consider the graph of $f(x)$. Is $-f(x)$ its horizontal or vertical reflection?
|
||||
Back: Vertical (reflection along the $x$-axis).
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938171-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose $f(x)$ has range $[4, 8]$. What is the domain of $-f(x)$?
|
||||
Back: The same as that of $f(x)$.
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938174-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose $f(x)$ has range $[4, 8]$. What is the range of $-f(x)$?
|
||||
Back: $[-8, -4]$
|
||||
Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html).
|
||||
<!--ID: 1734656938178-->
|
||||
END%%
|
||||
|
||||
## Bibliography
|
||||
|
||||
* “Cartesian Coordinate System,” in _Wikipedia_, October 21, 2024, [https://en.wikipedia.org/w/index.php?title=Cartesian_coordinate_system](https://en.wikipedia.org/w/index.php?title=Cartesian_coordinate_system&oldid=1252434514).
|
||||
|
|
|
|||
|
|
@ -12,8 +12,6 @@ tags:
|
|||
|
||||
Modern [[x86-64/index|x86-64]] Linux systems use the ELF (Executable and Linkable Format) object file format.
|
||||
|
||||
![[elf.png]]
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What object file format do modern x86-64 Linux machines typically use?
|
||||
|
|
@ -38,11 +36,46 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
|
|||
<!--ID: 1734356868446-->
|
||||
END%%
|
||||
|
||||
### Relocatable Object Files
|
||||
## Relocatable Object Files
|
||||
|
||||
A typical ELF relocatable object file contains the following sections:
|
||||
![[elf.png]]
|
||||
|
||||
#### `.text`
|
||||
%%ANKI
|
||||
Basic
|
||||
A relocatable object file is typically broken up into what three regions?
|
||||
Back: The header, sections, and the section header table.
|
||||
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
<!--ID: 1734456879220-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
In a relocatable object file, what exists between the header and section header table?
|
||||
Back: The sections.
|
||||
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
<!--ID: 1734456879305-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Cloze
|
||||
A relocatable object file consists of a {header}, {sections}, and a {section header table}, in that order.
|
||||
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
<!--ID: 1734456879322-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Where in a relocatable object file does the section header table exist?
|
||||
Back: At the end.
|
||||
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
<!--ID: 1734456879328-->
|
||||
END%%
|
||||
|
||||
## Sections
|
||||
|
||||
A typical ELF object file contains the following sections:
|
||||
|
||||
### `.text`
|
||||
|
||||
The machine code of the compiled program.
|
||||
|
||||
|
|
@ -69,7 +102,7 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
|
|||
<!--ID: 1734367304872-->
|
||||
END%%
|
||||
|
||||
#### `.rodata`
|
||||
### `.rodata`
|
||||
|
||||
Read-only data such as the format strings in [[c17/strings/printf|printf]] statements and [[conditions#JMP|jump tables]] for switch statements.
|
||||
|
||||
|
|
@ -114,7 +147,7 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
|
|||
<!--ID: 1734367304878-->
|
||||
END%%
|
||||
|
||||
#### `.data`
|
||||
### `.data`
|
||||
|
||||
Global and static C variables initialized to a non-zero value.
|
||||
|
||||
|
|
@ -187,7 +220,7 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
|
|||
<!--ID: 1734369188110-->
|
||||
END%%
|
||||
|
||||
#### `.bss`
|
||||
### `.bss`
|
||||
|
||||
Uninitialized global and static C variables, along with any global or static variables initialized to zero.
|
||||
|
||||
|
|
@ -298,7 +331,7 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
|
|||
<!--ID: 1734369188106-->
|
||||
END%%
|
||||
|
||||
#### `.symtab`
|
||||
### `.symtab`
|
||||
|
||||
A symbol table with information about functions and global variables defined and referenced in the program.
|
||||
|
||||
|
|
@ -326,6 +359,96 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
|
|||
<!--ID: 1734370180083-->
|
||||
END%%
|
||||
|
||||
### `.rel.text`
|
||||
|
||||
A list of locations in the `.text` section that will need to be modified when the linker combines this object file with others.
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What does the `.rel.text` section of an ELF file contain?
|
||||
Back: Relocation entries for the `.text` section.
|
||||
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
<!--ID: 1734456879344-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Why is the `.rel.text` ELF section named the way it is?
|
||||
Back: It's short for **rel**ocation entries for the `.text` section.
|
||||
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
<!--ID: 1734456879386-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Cloze
|
||||
The {`.rel.text`} section contains {relocation entries} for the `.text` section.
|
||||
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
<!--ID: 1734456879393-->
|
||||
END%%
|
||||
|
||||
### `.rel.data`
|
||||
|
||||
A list of locations in the `.data` section that will need to be modified when the linker combines this object file with others.
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What does the `.rel.data` section of an ELF file contain?
|
||||
Back: Relocation entries for the `.data` section.
|
||||
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
<!--ID: 1734456879404-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Why is the `.rel.data` ELF section named the way it is?
|
||||
Back: It's short for **rel**ocation entries for the `.data` section.
|
||||
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
<!--ID: 1734456879407-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Cloze
|
||||
The {`.rel.data`} section contains {relocation entries} for the `.data` section.
|
||||
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
<!--ID: 1734456879414-->
|
||||
END%%
|
||||
|
||||
### `.strtab`
|
||||
|
||||
A string table for the symbol tables in the `.symtab` section as well as for section names in the section headers. It is a sequence of `NUL`-terminated character strings.
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What does the `.strtab` section of an ELF file contain?
|
||||
Back: A string table.
|
||||
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
<!--ID: 1734456879418-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Why is the `.strtab` ELF section named the way it is?
|
||||
Back: It is short for **str**ing **tab**le.
|
||||
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
<!--ID: 1734456879422-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
The `.strtab` provides information for what other, non-debug ELF section?
|
||||
Back: `.symtab`
|
||||
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
<!--ID: 1734456879427-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Section names are contained in what ELF section?
|
||||
Back: `.strtab`
|
||||
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
<!--ID: 1734456879433-->
|
||||
END%%
|
||||
|
||||
## Bibliography
|
||||
|
||||
* Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
|
||||
|
|
@ -552,7 +552,7 @@ END%%
|
|||
%%ANKI
|
||||
Basic
|
||||
Suppose sets $A$ and $B$ are finite. When is $A \cup B$ infinite?
|
||||
Back: The union of two finite sets is always finite.
|
||||
Back: N/A. The union of two finite sets is always finite.
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1733675522739-->
|
||||
END%%
|
||||
|
|
@ -591,8 +591,8 @@ END%%
|
|||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose sets $A$ and $B$ are finite. When is $A \cap B$ finite?
|
||||
Back: The intersection of two finite sets is always finite.
|
||||
Suppose sets $A$ and $B$ are finite. When is $A \cap B$ infinite?
|
||||
Back: N/A. The intersection of two finite sets is always finite.
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1733675522748-->
|
||||
END%%
|
||||
|
|
@ -615,20 +615,12 @@ END%%
|
|||
|
||||
%%ANKI
|
||||
Basic
|
||||
Suppose sets $A$ and $B$ are finite. When is $A \times B$ finite?
|
||||
Back: The Cartesian product of two finite sets is always finite.
|
||||
Suppose sets $A$ and $B$ are finite. When is $A \times B$ infinite?
|
||||
Back: N/A. The Cartesian product of two finite sets is always finite.
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1733675522751-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $m, n \in \omega$ such that $A \approx m$ and $B \approx n$. What does $\mathop{\text{card}}(A \times B)$ evaluate to?
|
||||
Back: $m \cdot n$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1733693785295-->
|
||||
END%%
|
||||
|
||||
### Addition
|
||||
|
||||
Let $\kappa$ and $\lambda$ be any cardinal numbers. Then $\kappa + \lambda = \mathop{\text{card}}(K \cup L)$, where $K$ and $L$ are any disjoint sets of cardinality $\kappa$ and $\lambda$, respectively.
|
||||
|
|
@ -641,14 +633,6 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
|
|||
<!--ID: 1733710439132-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $K$ and $L$ be sets. What does $\mathop{\text{card}}(K \cup L)$ evaluate to?
|
||||
Back: N/A. $K$ and $L$ must be disjoint sets for evaluation to make sense.
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1733710439139-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $K$ and $L$ be disjoint sets. What does $\mathop{\text{card}}(K \cup L)$ evaluate to?
|
||||
|
|
@ -659,7 +643,7 @@ END%%
|
|||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $K \approx \kappa$ and $L \approx \lambda$. What is necessary for $\mathop{\text{card}}(K \cup L) \approx \kappa + \lambda$?
|
||||
Let $\mathop{\text{card}}(K) = \kappa$ and $\mathop{\text{card}}(L) = \lambda$. What is necessary for $\mathop{\text{card}}(K \cup L) = \kappa + \lambda$?
|
||||
Back: That $K$ and $L$ are disjoint.
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1733710439146-->
|
||||
|
|
@ -696,6 +680,62 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
|
|||
<!--ID: 1734374219325-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What cardinal number does $0 + \aleph_0$ evaluate to?
|
||||
Back: $\aleph_0$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487310-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Expression $0 + \aleph_0$ corresponds to the cardinality of what set?
|
||||
Back: $\varnothing \cup \omega$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487313-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $n \in \omega$. What cardinal number does $n^+ + \aleph_0$ evaluate to?
|
||||
Back: $\aleph_0$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487316-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $n \in \omega$. Expression $n + \aleph_0$ corresponds to the cardinality of what set?
|
||||
Back: $(n \times \{0\}) \cup (\omega \times \{1\})$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487319-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What cardinal number does $\aleph_0 + \aleph_0$ evaluate to?
|
||||
Back: $\aleph_0$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487326-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Expression $\aleph_0 + \aleph_0$ corresponds to the cardinality of what set?
|
||||
Back: $(\omega \times \{0\}) \cup (\omega \times \{1\})$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487330-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $\kappa$ be a cardinal number. What cardinal number does $\kappa + 0$ evaluate to?
|
||||
Back: $0$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487333-->
|
||||
END%%
|
||||
|
||||
### Multiplication
|
||||
|
||||
Let $\kappa$ and $\lambda$ be any cardinal numbers. Then $\kappa \cdot \lambda = \mathop{\text{card}}(K \times L)$, where $K$ and $L$ are any sets of cardinality $\kappa$ and $\lambda$, respectively.
|
||||
|
|
@ -731,6 +771,14 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
|
|||
<!--ID: 1733710439162-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $m, n \in \omega$ such that $A \approx m$ and $B \approx n$. What does $\mathop{\text{card}}(A \times B)$ evaluate to?
|
||||
Back: $m \cdot n$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1733693785295-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
How do we prove $2 \cdot 2 = 4$ using the recursion theorem?
|
||||
|
|
@ -755,6 +803,70 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
|
|||
<!--ID: 1734374219328-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What cardinal number does $0 \cdot \aleph_0$ evaluate to?
|
||||
Back: $0$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487336-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Expression $0 \cdot \aleph_0$ corresponds to the cardinality of what set?
|
||||
Back: $\varnothing \times \omega$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487339-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $n \in \omega$. What cardinal number does $n^+ \cdot \aleph_0$ evaluate to?
|
||||
Back: $\aleph_0$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487342-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $n \in \omega$. Expression $n \cdot \aleph_0$ corresponds to the cardinality of what set?
|
||||
Back: $n \times \omega$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487345-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What cardinal number does $\aleph_0 \cdot \aleph_0$ evaluate to?
|
||||
Back: $\aleph_0$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487349-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Expression $\aleph_0 \cdot \aleph_0$ corresponds to the cardinality of what set?
|
||||
Back: $\omega \times \omega$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487352-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $\kappa$ be a cardinal number. What cardinal number does $\kappa \cdot 0$ evaluate to?
|
||||
Back: $0$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487356-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $\kappa$ be a cardinal number. What cardinal number does $\kappa \cdot 1$ evaluate to?
|
||||
Back: $\kappa$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487359-->
|
||||
END%%
|
||||
|
||||
### Exponentiation
|
||||
|
||||
Let $\kappa$ and $\lambda$ be any cardinal numbers. Then $\kappa^\lambda = \mathop{\text{card}}(^LK)$, where $K$ and $L$ are any sets of cardinality $\kappa$ and $\lambda$, respectively.
|
||||
|
|
@ -822,6 +934,62 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
|
|||
<!--ID: 1734374219332-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What cardinal number does $0^{\aleph_0}$ evaluate to?
|
||||
Back: $0$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487363-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Expression $0^{\aleph_0}$ corresponds to the cardinality of what set?
|
||||
Back: $^\omega \varnothing$
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487368-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $\kappa$ be a nonzero cardinal number. What cardinal number does $0^\kappa$ evaluate to?
|
||||
Back: $0$.
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487372-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
What cardinal number does $0^0$ evaluate to?
|
||||
Back: $1$.
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487376-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $\kappa$ be a cardinal number. Expression $0^\kappa$ corresponds to the cardinality of what set?
|
||||
Back: $^K\varnothing$ where $\mathop{\text{card}} K = \kappa$.
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487381-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $\kappa$ be a cardinal number. What cardinal number does $\kappa^0$ evaluate to?
|
||||
Back: $1$.
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487384-->
|
||||
END%%
|
||||
|
||||
%%ANKI
|
||||
Basic
|
||||
Let $\kappa$ be a cardinal number. Expression $\kappa^0$ corresponds to the cardinality of what set?
|
||||
Back: $^\varnothing K$ where $\mathop{\text{card}} K = \kappa$..
|
||||
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
<!--ID: 1734520487388-->
|
||||
END%%
|
||||
|
||||
## Bibliography
|
||||
|
||||
* Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
|
||||
Loading…
Reference in New Issue