LUBs and x86 registers.

notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json

@@ -502,7 +502,7 @@
     "set/axioms.md": "063955bf19c703e9ad23be2aee4f1ab7",
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-    "x86-64/registers.md": "4bcc04cea66b37d404ac430b0f034697",
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-    "_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 @@
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-    "set/order.md": "373f4336d4845a3c2188d2215ac5fbc4",
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-    "_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": [

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.
+* Notes on [[registers|condition code registers]] and a [[conditions|few instruction classes]] that explicitly update them.

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]].

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)
+- [ ] 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.

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).
+<!--ID: 1724115133063-->
+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).
+<!--ID: 1724115335382-->
+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).
+<!--ID: 1724115335387-->
+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).
+<!--ID: 1724115335393-->
+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).
+<!--ID: 1724115133068-->
+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).
+<!--ID: 1724115133071-->
+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).
+<!--ID: 1724115133074-->
+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).
+<!--ID: 1724115133077-->
+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).
+<!--ID: 1724115133080-->
+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).
+<!--ID: 1724115133084-->
+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).
+<!--ID: 1724115133087-->
+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).
+<!--ID: 1724115133090-->
+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).
+<!--ID: 1724115133094-->
+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).
+<!--ID: 1724115133110-->
+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).
+<!--ID: 1724115133099-->
+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).
+<!--ID: 1724115133103-->
+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).
+<!--ID: 1724115133106-->
+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).
+<!--ID: 1724115335395-->
+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).
+<!--ID: 1724115335390-->
+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).
+<!--ID: 1724115953300-->
+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).
+<!--ID: 1724115953329-->
+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).
+<!--ID: 1724115953335-->
+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).
+<!--ID: 1724115953341-->
+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).
+<!--ID: 1724115953346-->
+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).
+<!--ID: 1724115953352-->
+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).
+<!--ID: 1724115953358-->
+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).
+<!--ID: 1724115953364-->
+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).
+<!--ID: 1724115953369-->
+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).
+<!--ID: 1724115953375-->
+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).
+<!--ID: 1724115953380-->
+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).
+<!--ID: 1724115953386-->
+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).
+<!--ID: 1724116323038-->
+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).
+<!--ID: 1724116323044-->
+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).
+<!--ID: 1724116323046-->
+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).
+<!--ID: 1724116323049-->
+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).
+<!--ID: 1724116323052-->
+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).
+<!--ID: 1724116323055-->
+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).
+<!--ID: 1724115953392-->
+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).
+<!--ID: 1724115953397-->
+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).
+<!--ID: 1724115953402-->
+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).
+<!--ID: 1724115953408-->
+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).
+<!--ID: 1724115953417-->
+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).
+<!--ID: 1724115953422-->
+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).
+<!--ID: 1724115953428-->
+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).
+<!--ID: 1724115953433-->
+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).
+<!--ID: 1724115953438-->
+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).
+<!--ID: 1724115953443-->
+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).
+<!--ID: 1724115953448-->
+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).
+<!--ID: 1724115953452-->
+END%%
+
+## Bibliography
+
+* Tom M. Apostol, _Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra_, 2nd ed. (New York: Wiley, 1980).

notes/calculus/index.md

@@ -0,0 +1,3 @@
+---
+title: Calculus
+---

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).
 <!--ID: 1721696946377-->
 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).

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     |

notes/x86-64/registers.md

@@ -83,6 +83,210 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
 <!--ID: 1713212889874-->
 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.
+<!--ID: 1724119420029-->
+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.
+<!--ID: 1724119420032-->
+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.
+<!--ID: 1724119420035-->
+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.
+<!--ID: 1724119420039-->
+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.
+<!--ID: 1724119420043-->
+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.
+<!--ID: 1724119420047-->
+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.
+<!--ID: 1724119420052-->
+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.
+<!--ID: 1724119420056-->
+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.
+<!--ID: 1724119420060-->
+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.
+<!--ID: 1724119420064-->
+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.
+<!--ID: 1724119420068-->
+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.
+<!--ID: 1724119420071-->
+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.
+<!--ID: 1724119420075-->
+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.
+<!--ID: 1724119420079-->
+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.
+<!--ID: 1724119420082-->
+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.
+<!--ID: 1724119420086-->
+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.
+<!--ID: 1724119420090-->
+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.
+<!--ID: 1724119420093-->
+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.
+<!--ID: 1724119420096-->
+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.
+<!--ID: 1724119420100-->
+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.
+<!--ID: 1724119420103-->
+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.
+<!--ID: 1724119420106-->
+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.
+<!--ID: 1724119420109-->
+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.
+<!--ID: 1724119420113-->
+END%%
+
+%%ANKI
+Basic
+From smallest to largest, list the four "return value" registers.
+Back: `%al`, `%ax`, `%eax`, and `$rax`.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1724119420117-->
+END%%
+
+%%ANKI
+Basic
+From smallest to largest, list the four "stack pointer" registers.
+Back: `%spl`, `%sp`, `%esp`, and `$rsp`.
+Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
+<!--ID: 1724119420122-->
+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