diff --git a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json index f1f965f..40bc570 100644 --- a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json +++ b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json @@ -502,7 +502,7 @@ "set/axioms.md": "063955bf19c703e9ad23be2aee4f1ab7", "_journal/2024-05-14.md": "f6ece1d6c178d57875786f87345343c5", "_journal/2024-05/2024-05-13.md": "71eb7924653eed5b6abd84d3a13b532b", - "x86-64/registers.md": "4bcc04cea66b37d404ac430b0f034697", + "x86-64/registers.md": "e55217fb711495490546975a7828e8f1", "_journal/2024-05-15.md": "4e6a7e6df32e93f0d8a56bc76613d908", "_journal/2024-05/2024-05-14.md": "f6ece1d6c178d57875786f87345343c5", "_journal/2024-05-16.md": "580c7ec61ec56be92fa8d6affcf0a5f6", @@ -576,7 +576,7 @@ "_journal/2024-06-09.md": "935b3ddf65c51e680ac5c000c7e380af", "_journal/2024-06/2024-06-08.md": "9e1ebc8882a395b96ca765ad5c982d68", "_journal/2024-06-10.md": "84d27300b97c8544ab4ec68b06edd824", - "_journal/2024-06/2024-06-09.md": "4c336a39775846b416aa73278435065f", + "_journal/2024-06/2024-06-09.md": "7c197f5f2ce193cfbc60f9c8168c9996", "_journal/2024-06-11.md": "48f46f654a1b8dfeebc01b3adb2bc1d1", "_journal/2024-06/2024-06-10.md": "1fe3a8beb03b1cc9af188b85933339e4", "_journal/2024-06-12.md": "8cc810c0f594093768117f57461e2e9e", @@ -647,7 +647,7 @@ "_journal/2024-07/2024-07-11.md": "298cc3688675ee669b5a51d545fd61b5", "_journal/2024-07/2024-07-10.md": "a0fe22d8be519bf435a5949999eeb4de", "_journal/2024-07-13.md": "13b5101306b5542b8a1381a6477378ca", - "_journal/2024-07/2024-07-12.md": "6603ed8a3f9a9e87bf40e81b03e96356", + "_journal/2024-07/2024-07-12.md": "8073584fae2fe7bffcd4b69a7cd29058", "hashing/static.md": "3ec6eaee73fb9b599700f5a56b300b83", "hashing/addressing.md": "01b33abe25aae285e1641fa43470065b", "ontology/index.md": "0994403dcd84415f1459752129b55f65", @@ -747,12 +747,15 @@ "_journal/2024-08/2024-08-15.md": "7c3a96a25643b62b0064bf32cb17d92f", "_journal/2024-08-17.md": "b06a551560c377f61a1b39286cd43cee", "_journal/2024-08/2024-08-16.md": "096d9147a9e3e7a947558f8dec763a2c", - "set/order.md": "373f4336d4845a3c2188d2215ac5fbc4", + "set/order.md": "49fcebf2e20a6f73571fea5ff09f0753", "_journal/2024-08-18.md": "6f8aec69e00401b611db2a377a3aace5", "ontology/philosophy/properties.md": "41b32249d3e4c23d73ddb3a417d65a4c", - "_journal/2024-08-19.md": "e233a2225fdf95a161614e0bc22fce20", + "_journal/2024-08-19.md": "82d3bfa01b4187a56a418f6e33bd10b3", "_journal/2024-08/2024-08-18.md": "6f8aec69e00401b611db2a377a3aace5", - "_journal/2024-08/2024-08-17.md": "b06a551560c377f61a1b39286cd43cee" + "_journal/2024-08/2024-08-17.md": "b06a551560c377f61a1b39286cd43cee", + "calculus/bounds.md": "4add5fb7591087d0b3383c53dc62e365", + "calculus/index.md": "5ee4d950533ae330ca5ef9e113fe87f3", + "x86-64/instructions/conditions.md": "c5571deac40ac2eeb8666f2d3b3c278e" }, "fields_dict": { "Basic": [ diff --git a/notes/_journal/2024-06/2024-06-09.md b/notes/_journal/2024-06/2024-06-09.md index fb0856c..cf0acf6 100644 --- a/notes/_journal/2024-06/2024-06-09.md +++ b/notes/_journal/2024-06/2024-06-09.md @@ -8,4 +8,4 @@ title: "2024-06-09" - [ ] Sheet Music (10 min.) - [ ] Korean (Read 1 Story) -* Notes on [[registers|condition code registers]] and a [[condition-codes|few instruction classes]] that explicitly update them. \ No newline at end of file +* Notes on [[registers|condition code registers]] and a [[conditions|few instruction classes]] that explicitly update them. \ No newline at end of file diff --git a/notes/_journal/2024-07/2024-07-12.md b/notes/_journal/2024-07/2024-07-12.md index 4632fdd..f6f9c8d 100644 --- a/notes/_journal/2024-07/2024-07-12.md +++ b/notes/_journal/2024-07/2024-07-12.md @@ -9,5 +9,5 @@ title: "2024-07-12" - [ ] Korean (Read 1 Story) * Notes on [[set#Index Sets|index sets]] and [[set#Function Sets|function sets]]. -* Notes on a few of the [[condition-codes#SET|set]] instructions. +* Notes on a few of the [[conditions#SET|set]] instructions. * Small collection of notes on [[hashing/index#Static Hashing|static hashing]]. \ No newline at end of file diff --git a/notes/_journal/2024-08-19.md b/notes/_journal/2024-08-19.md index de94701..1b65940 100644 --- a/notes/_journal/2024-08-19.md +++ b/notes/_journal/2024-08-19.md @@ -4,6 +4,10 @@ title: "2024-08-19" - [x] Anki Flashcards - [x] KoL -- [ ] OGS +- [x] OGS - [ ] Sheet Music (10 min.) -- [ ] Korean (Read 1 Story) \ No newline at end of file +- [ ] Korean (Read 1 Story) + +* [[bounds|Notes]] on (least) upper bounds and (greatest) lower bounds. +* Finished exercises 3.13 and 3.14 in "Computer systems a programmer's perspective". +* Add notes on `%rax` and `%rsp` registers. \ No newline at end of file diff --git a/notes/calculus/bounds.md b/notes/calculus/bounds.md new file mode 100644 index 0000000..7d6aa6f --- /dev/null +++ b/notes/calculus/bounds.md @@ -0,0 +1,421 @@ +--- +title: Bounds +TARGET DECK: Obsidian::STEM +FILE TAGS: calculus::bounds +tags: + - calculus +--- + +## Overview + +Suppose $S$ is a nonempty set of real numbers and suppose there are numbers $L$ and $U$ such that $L \leq x \leq U$ for all $x \in S$. Then $S$ is said to be **bounded below** by $L$ and **bounded above** by $U$. The number $L$ is said to be a **lower bound** for $S$; the number $U$ is said to be an **upper bound** for $S$. + +%%ANKI +Basic +Let $\varnothing \subset S \subseteq \mathbb{R}$. What does it mean for $S$ to be bounded below by $B$? +Back: For all $x \in S$, $B \leq x$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What does it mean for $\varnothing \subseteq \mathbb{R}$ to be bounded above by $B$? +Back: N/A. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Suppose $S \subseteq \mathbb{R}$ is bounded below by $B$. What kind of mathematical object is $S$? +Back: A nonempty set. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Suppose $S \subseteq \mathbb{R}$ is unbounded above. What kind of mathematical object is $S$? +Back: A set (possibly empty). +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Is the set of positive real numbers bounded below? +Back: Yes. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Let $\varnothing \subset S \subseteq \mathbb{R}$. What does it mean for $S$ to be bounded above by $B$? +Back: For all $x \in S$, $x \leq B$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Is the set of positive real numbers bounded above? +Back: No. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What are the upper bounds of interval $[0, 1] \subseteq \mathbb{R}$? +Back: All real numbers $x \geq 1$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What are the upper bounds of interval $(0, 1) \subseteq \mathbb{R}$? +Back: All real numbers $x \geq 1$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What are the lower bounds of interval $[0, 1] \subseteq \mathbb{R}$? +Back: All real numbers $x \leq 0$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What are the lower bounds of interval $(0, 1) \subseteq \mathbb{R}$? +Back: All real numbers $x \leq 0$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +If $L \in S$, then $L$ is the **minimum element** of $S$ (denoted $L = \mathop{\text{min}} S$). Likewise, if $U \in S$, then $U$ is the **maximum element** of $S$ (denoted $U = \mathop{\text{max}}S$). A set with no lower bound is said to be **unbounded below**. A set with no upper bound is said to be **unbounded above**. + +%%ANKI +Basic +What is a maximum element of set $\varnothing \subset S \subseteq \mathbb{R}$? +Back: A member of $S$ that is also an upper bound. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What is the maximum element of interval $[0, 1] \subseteq \mathbb{R}$? +Back: $1$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What is the maximum element of interval $(0, 1) \subseteq \mathbb{R}$? +Back: N/A. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What is a minimum element of set $\varnothing \subset S \subseteq \mathbb{R}$? +Back: A member of $S$ that is also a lower bound. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What is the minimum element of interval $(0, 1) \subseteq \mathbb{R}$? +Back: N/A. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What is the minimum element of interval $[0, 1] \subseteq \mathbb{R}$? +Back: $0$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +How is a maximum element of $\varnothing \subset S \subseteq \mathbb{R}$ denoted? +Back: As $\mathop{\text{max}} S$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +How is a minimum element of $\varnothing \subset S \subseteq \mathbb{R}$ denoted? +Back: As $\mathop{\text{min}} S$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +## Least Upper Bounds + +A number $B$ is called a **least upper bound** (or **supremum**) of a nonempty set $S$ if $B$ is an upper bound for $S$ and no number less than $B$ is an upper bound for $S$. This is denoted as $B = \mathop{\text{lub}}S$ or $B = \mathop{\text{sup}} S$. + +%%ANKI +Basic +Let $\varnothing \subset S \subseteq \mathbb{R}$. What is a least upper bound of $S$? +Back: An upper bound $B$ for $S$ such that no number less than $B$ is also an upper bound for $S$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What is an alternative term for a least upper bound of $S$? +Back: A supremum of $S$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +How is a least upper bound for $S$ denoted? +Back: As $\mathop{\text{lub}} S$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +How is a supremum for $S$ denoted? +Back: As $\mathop{\text{sup}} S$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What distinguishes a supremum from a least upper bound? +Back: They are synonyms of one another. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What distinguishes a supremum from a maximum? +Back: A supremum is not necessarily a member of the reference set. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What is the least upper bound of interval $[0, 1] \subseteq \mathbb{R}$? +Back: $1$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What is the supremum of interval $(0, 1) \subseteq \mathbb{R}$? +Back: $1$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +How many upper bounds can a nonempty subset of $\mathbb{R}$ have? +Back: $0$ or more. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +How many supremums can a nonempty subset of $\mathbb{R}$ have? +Back: $0$ or $1$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Is a maximum of a nonempty subset $S$ of $\mathbb{R}$ a supremum of $S$? +Back: Yes. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Is a least upper bound of a nonempty subset $S$ of $\mathbb{R}$ a maximum of $S$? +Back: Not necessarily. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +### Completeness Axiom + +Every nonempty set $S$ of real numbers which is bounded above has a supremum; that is, there is a real number $B$ such that $B = \mathop{\text{sup}} S$. + +%%ANKI +Basic +What does the completeness axiom of real numbers state? +Back: Every nonempty set of real numbers bounded above has a supremum. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Consider $\varnothing \subseteq \mathbb{R}$. Why doesn't the completeness axiom of real numbers apply? +Back: It only applies to nonempty sets. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Consider $(0, 1) \subseteq \mathbb{R}$. Why doesn't the completeness axiom of real numbers apply? +Back: N/A. It does. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Consider $\mathbb{R}^+$. Why doesn't the completeness axiom apply? +Back: It only applies to nonempty sets that are bounded above. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Consider $(-\infty, 0)$. Why doesn't the completeness axiom apply? +Back: N/A. It does. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What arbitrary decision was made when formulating the completeness axiom of real numbers? +Back: Whether to use supremums or infimums. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +## Greatest Lower Bounds + +A number $B$ is called a **greatest lower bound** (or **infimum**) of a nonempty set $S$ if $B$ is a lower bound for $S$ and no number greater than $B$ is a lower bound for $S$. This is denoted as $B = \mathop{\text{glb}} S$ or $B = \mathop{\text{inf}} S$. + +%%ANKI +Basic +Let $\varnothing \subset S \subseteq \mathbb{R}$. What is a greatest upper bound of $S$? +Back: A lower bound $B$ for $S$ such that no number greater than $B$ is also a lower bound for $S$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What is an alternative term for a greatest lower bound of $S$? +Back: An infimum of $S$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +How is a greatest lower bound for $S$ denoted? +Back: As $\mathop{\text{glb}} S$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +How is an infimum for $S$ denoted? +Back: As $\mathop{\text{inf}} S$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What distinguishes a greatest lower bound from an infimum? +Back: They are synonyms of one another. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What distinguishes an infimum from a minimum? +Back: A supremum is not necessarily a member of the reference set. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What is the infimum of interval $[0, 1] \subseteq \mathbb{R}$? +Back: $0$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +What is the greatest lower bound of interval $(0, 1) \subseteq \mathbb{R}$? +Back: $0$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +How many lower bounds can a nonempty subset of $\mathbb{R}$ have? +Back: $0$ or more. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +How many greatest lower bounds can a nonempty subset of $\mathbb{R}$ have? +Back: $0$ or $1$. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Is an infimum of a nonempty subset $S$ of $\mathbb{R}$ a minimum of $S$? +Back: Not necessarily. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +%%ANKI +Basic +Is a minimum of a nonempty subset $S$ of $\mathbb{R}$ a greatest lower bound of $S$? +Back: Yes. +Reference: Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). + +END%% + +## Bibliography + +* Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980). \ No newline at end of file diff --git a/notes/calculus/index.md b/notes/calculus/index.md new file mode 100644 index 0000000..9ab0787 --- /dev/null +++ b/notes/calculus/index.md @@ -0,0 +1,3 @@ +--- +title: Calculus +--- diff --git a/notes/set/order.md b/notes/set/order.md index 43bc2a4..2d4a59a 100644 --- a/notes/set/order.md +++ b/notes/set/order.md @@ -647,7 +647,7 @@ END%% Basic What name is given to a member of a partition of a set? Back: A cell. -Reference: “Partition of a Set,” in _Wikipedia_, June 18, 2024, [https://en.wikipedia.org/w/index.php?title=Partition_of_a_set](https://en.wikipedia.org/w/index.php?title=Partition_of_a_set&oldid=1229656401). +Reference: John B. Fraleigh, _A First Course in Abstract Algebra_, Seventh edition, Pearson new international edition (Harlow: Pearson, 2014). END%% @@ -959,6 +959,7 @@ END%% * “Equivalence Relation,” in _Wikipedia_, July 21, 2024, [https://en.wikipedia.org/w/index.php?title=Equivalence_relation](https://en.wikipedia.org/w/index.php?title=Equivalence_relation&oldid=1235801091). * Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). +* John B. Fraleigh, _A First Course in Abstract Algebra_, Seventh edition, Pearson new international edition (Harlow: Pearson, 2014). * “Partially Ordered Set,” in _Wikipedia_, June 22, 2024, [https://en.wikipedia.org/w/index.php?title=Partially_ordered_set](https://en.wikipedia.org/w/index.php?title=Partially_ordered_set&oldid=1230452839). * “Partition of a Set,” in _Wikipedia_, June 18, 2024, [https://en.wikipedia.org/w/index.php?title=Partition_of_a_set](https://en.wikipedia.org/w/index.php?title=Partition_of_a_set&oldid=1229656401). * “Preorder,” in _Wikipedia_, July 21, 2024, [https://en.wikipedia.org/w/index.php?title=Preorder](https://en.wikipedia.org/w/index.php?title=Preorder&oldid=1235839474). diff --git a/notes/x86-64/instructions/condition-codes.md b/notes/x86-64/instructions/conditions.md similarity index 99% rename from notes/x86-64/instructions/condition-codes.md rename to notes/x86-64/instructions/conditions.md index 99f67af..62e0158 100644 --- a/notes/x86-64/instructions/condition-codes.md +++ b/notes/x86-64/instructions/conditions.md @@ -1,5 +1,5 @@ --- -title: Condition Code Operations +title: Condition Operations TARGET DECK: Obsidian::STEM FILE TAGS: x86-64 tags: @@ -8,6 +8,10 @@ tags: ## Overview +A number of instructions operate with respect to the [[registers#Condition Codes|condition code registers]]. + +## CMP and TEST + | Instruction | Operands | Based On | Description | | ------------ | ---------- | --------------------- | ----------- | | `cmp[bwlq]` | $S_1, S_2$ | $S_2 - S_1$ | Compare | diff --git a/notes/x86-64/registers.md b/notes/x86-64/registers.md index 73bc32b..e0f0a21 100644 --- a/notes/x86-64/registers.md +++ b/notes/x86-64/registers.md @@ -83,6 +83,210 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program END%% +%%ANKI +Basic +How many bytes make up the `%rax` register? +Back: $8$. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Basic +How many bytes make up the `%ax` register? +Back: $2$. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Basic +How many bytes make up the `%al` register? +Back: $1$. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Basic +How many bytes make up the `%eax` register? +Back: $4$. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Cloze +{1:Double words} are to {2:`%eax`} whereas {2:quad words} are to {1:`%rax`}. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Cloze +{1:Words} are to {2:`%ax`} whereas {2:bytes} are to {1:`%al`}. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Basic +How do you access the low-order 2 bytes of `%rax`? +Back: By using `%ax`. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Basic +How do you access the low-order 4 bytes of `%rax`? +Back: By using `%eax`. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Basic +How do you access the low-order byte of `%rax`? +Back: By using `%al`. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Cloze +By convention, register {`%rax`} is used for {return values}. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Basic +How many bytes make up the `%rsp` register? +Back: $8$. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Basic +How many bytes make up the `%sp` register? +Back: $2$. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Basic +How many bytes make up the `%spl` register? +Back: $1$. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Basic +How many bytes make up the `%esp` register? +Back: $4$. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Cloze +{1:Words} are to {2:`%sp`} whereas {2:double words} are to {1:`%esp`}. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Cloze +{1:Bytes} are to {2:`%spl`} whereas {2:quad words} are to {1:`%rsp`}. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Basic +How do you access the low-order 2 bytes of `%rsp`? +Back: By using `%sp`. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Basic +How do you access the low-order 4 bytes of `%rsp`? +Back: By using `%esp`. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Basic +How do you access the low-order byte of `%rsp`? +Back: By using `%spl`. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Cloze +By convention, register {`%rsp`} is used for {the stack pointer}. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Cloze +Which register should I use for an 2 byte return value? +Back: `%ax` +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Cloze +Which register should I use for a 1 byte stack pointer? +Back: `%spl` +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Cloze +Which register should I use for a 4 byte stack pointer? +Back: `%esp` +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Cloze +Which register should I use for an 8 byte return value? +Back: `%rax` +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Basic +From smallest to largest, list the four "return value" registers. +Back: `%al`, `%ax`, `%eax`, and `$rax`. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +%%ANKI +Basic +From smallest to largest, list the four "stack pointer" registers. +Back: `%spl`, `%sp`, `%esp`, and `$rsp`. +Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. + +END%% + +## Condition Codes + The CPU also maintains a set of single-bit **condition code** registers describing attributes of the most recent arithmetic or logical operation. Code | Name | Description