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More floating-point notes.

c-declarations
Joshua Potter 2024-03-18 08:19:55 -04:00
parent 444418d78e
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---
title: "2024-03-17"
---
- [x] Anki Flashcards
- [x] KoL
- [ ] Sheet Music (10 min.)
- [ ] Go (1 Life & Death Problem)
- [ ] Korean (Read 1 Story)
- [ ] Interview Prep (1 Practice Problem)
- [ ] Log Work Hours (Max 3 hours)
* Finished translating `printf` to all relevant flashcards.
* Finish chapter 2 of "Computer Systems: A Programmer's Perspective".
* Last portion was on floating-point encoding.

0
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notes/c17/declarations.md
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@ -232,6 +232,14 @@ Reference: Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems
<!--ID: 1708631820826--> <!--ID: 1708631820826-->
END%% END%%
%%ANKI
Basic
How do we specify an octal integer literal?
Back: Prepend the literal with a `0`.
Reference: Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710673807992-->
END%%
%%ANKI %%ANKI
Basic Basic
Why avoid negative octal integer literals? Why avoid negative octal integer literals?
@ -240,6 +248,21 @@ Reference: Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems
<!--ID: 1708631820829--> <!--ID: 1708631820829-->
END%% END%%
%%ANKI
Basic
How do we specify a hexadecimal integer literal?
Back: Prepend the literal with a `0x` or `0X`.
Reference: Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710673807995-->
END%%
%%ANKI
Cloze
Octal literals are to {`0`} whereas hexadecimal literals are to {`0x`/`0X`}.
Reference: Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710673807997-->
END%%
%%ANKI %%ANKI
Basic Basic
Why avoid negative hexadecimal integer literals? Why avoid negative hexadecimal integer literals?

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@ -80,12 +80,13 @@ Tags: printf
<!--ID: 1708425941269--> <!--ID: 1708425941269-->
END%% END%%
| Flag | Description | Flag | Description
| ---- | -------------------------------------------------- | ---- | -----------
| `-` | Left-aligns the output | `-` | Left-aligns the output
| `+` | Prepends a plus for positive signed-numeric types | `+` | Prepends a plus for positive signed-numeric types
| `␣` | Prepends a space for positive signed-numeric types | `␣` | Prepends a space for positive signed-numeric types
| `0` | Prepends zeros for numeric types | `0` | Prepends zeros for numeric types
`#` | For `g` and `G`, trailing zeros are not removed. For `f`, `F`, `e`, `E`, `g`, and `G`, output always has a decimal point. For `o`, `x`, and `X`, the text `0`, `0x`, and `0X` is prepended to non-zero numbers respectively.
%%ANKI %%ANKI
Cloze Cloze
@ -272,6 +273,77 @@ Tags: printf
<!--ID: 1707918756888--> <!--ID: 1707918756888-->
END%% END%%
%%ANKI
Basic
How is `%#g` different from `%g`?
Back: The former always includes a decimal point and may include trailing `0`s.
Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
Tags: printf
<!--ID: 1710673807973-->
END%%
%%ANKI
Basic
How is `%#f` different from `%f`?
Back: The former always includes a decimal point.
Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
Tags: printf
<!--ID: 1710673807976-->
END%%
%%ANKI
Basic
How is `%#e` different from `%e`?
Back: The former always includes a decimal point.
Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
Tags: printf
<!--ID: 1710673807979-->
END%%
%%ANKI
Basic
Which `printf` flag can be used to ensure decimal points in the output of floating-point types?
Back: `#`
Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
Tags: printf
<!--ID: 1710673807981-->
END%%
%%ANKI
Basic
How is `%#o` different from `%o`?
Back: The former prepends a `0` to the output.
Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
Tags: printf
<!--ID: 1710673807983-->
END%%
%%ANKI
Basic
How is `%#x` different from `%x`?
Back: The former prepends a `0x` to the output.
Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
Tags: printf
<!--ID: 1710673807986-->
END%%
%%ANKI
Basic
How is `%#X` different from `%X`?
Back: The former prepends a `0X` to the output.
Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
Tags: printf
<!--ID: 1710673807988-->
END%%
%%ANKI
Cloze
`%#o` is to {`0`} as `%#x` is to {`0x`}.
Reference: “Printf,” in *Wikipedia*, January 18, 2024, [https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962](https://en.wikipedia.org/w/index.php?title=Printf&oldid=1196716962).
Tags: printf
<!--ID: 1710673807990-->
END%%
Length | Description Length | Description
--------- | ----------- --------- | -----------
`hh` | `int` sized integer argument promoted from a `char` `hh` | `int` sized integer argument promoted from a `char`
@ -488,6 +560,42 @@ Tags: printf
<!--ID: 1710450347012--> <!--ID: 1710450347012-->
END%% END%%
%%ANKI
Basic
Assuming round-to-even, what is the output of `printf("%.0f", 3.5)`?
Back: `4`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: printf
<!--ID: 1710675908301-->
END%%
%%ANKI
Basic
Assuming round-to-even, what is the output of `printf("%.0f", 2.5)`?
Back: `2`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: printf
<!--ID: 1710675908304-->
END%%
%%ANKI
Basic
How does the C standard define the rounding mode of floating-point specifiers?
Back: This is implementation specific.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: printf
<!--ID: 1710675908306-->
END%%
%%ANKI
Basic
What does the rounding mode of floating-point specifiers refer to?
Back: How numbers with greater than the specified precision are output.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: printf
<!--ID: 1710675908307-->
END%%
%%ANKI %%ANKI
Basic Basic
What three special identifiers might specifier `%F` output? What three special identifiers might specifier `%F` output?

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@ -1,5 +1,5 @@
--- ---
title: Float Encoding title: Floating Point
TARGET DECK: Obsidian::STEM TARGET DECK: Obsidian::STEM
FILE TAGS: binary::float ieee FILE TAGS: binary::float ieee
tags: tags:
@ -10,18 +10,22 @@ tags:
## Overview ## Overview
The IEEE floating-point standard defines an encoding used to represent numbers of form $$(-1)^s \times M \times 2^E$$ where $s$ denotes the **sign bit**, $M$ the **significand**, and $E$ the **exponent**. The binary representation of floating point numbers are segmented into three fields: the sign bit, the exponent field, and the fraction field. Furthermore, there are two forms these fields are interpreted with respect to: The IEEE floating-point standard defines an encoding used to represent numbers of form $$(-1)^s \times M \times 2^E$$ where $s$ denotes the **sign bit**, $M$ the **significand**, and $E$ the **exponent**. The binary representation of floating point numbers are segmented into three fields: the sign bit, the exponent field, and the fraction field. Furthermore, there are three classes these fields are interpreted with respect to:
* Normalized Form * Normalized Form
* Here the exponent field is neither all `0`s nor all `1`s. * Here the exponent field is neither all `0`s nor all `1`s.
* The significand is $1 + f$, where $f$ denotes the fractional part. * The significand is $1 + f$, where $f$ denotes the fractional part.
* $E = e - Bias$ where $e$ is the unsigned interpretation of the exponent field. * $E = e - Bias$ where $e$ is the unsigned interpretation of the exponent field.
* Denormalized Form * Denormalized Form
* Here the exponent field is either all `0`s or all `1`s. * Here the exponent field is all `0`s.
* The significand is $f$, where $f$ denotes the fractional part. * The significand is $f$, where $f$ denotes the fractional part.
* $E = 1 - Bias$, defined for smooth transition between normalized and denormalized values. * $E = 1 - Bias$, defined for smooth transition between normalized and denormalized values.
* Special Values
* Here the exponent field is all `1`s.
* If the fraction field is all `0`s, we have an $\infty$ value.
* If the fraction field is not all `0`s, we have $NaN$.
The $Bias$ in both forms is set to $2^{k - 1} - 1$ where $k$ denotes the number of bits that make up the exponent field. In C, fields have the following widths: The $Bias$ in the first two forms is set to $2^{k - 1} - 1$ where $k$ denotes the number of bits that make up the exponent field. In C, fields have the following widths:
Declaration | Sign Bit | Exponent Field | Fractional Field Declaration | Sign Bit | Exponent Field | Fractional Field
----------- | -------- | -------------- | ---------------- ----------- | -------- | -------------- | ----------------
@ -158,7 +162,7 @@ END%%
%%ANKI %%ANKI
Basic Basic
What IEEE standard describes floating point operations? What IEEE standard (number) describes floating point operations?
Back: 754 Back: 754
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710556914957--> <!--ID: 1710556914957-->
@ -167,7 +171,7 @@ END%%
%%ANKI %%ANKI
Basic Basic
What alternative name does IEEE Standard 754 go by? What alternative name does IEEE Standard 754 go by?
Back: IEEE floating point Back: IEEE floating-point
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710556914959--> <!--ID: 1710556914959-->
END%% END%%
@ -256,7 +260,7 @@ END%%
%%ANKI %%ANKI
Basic Basic
What visualization explains why $0.11\cdots1_2 = 1 - 2^{-n}$? What visualization explains why $0.11\cdots1_2 = 1 - 2^{-n}$?
Back: Each additional $1$ halves the remaining interval. Back: Each additional $1$ adds half of the remaining interval to a running total.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710556914982--> <!--ID: 1710556914982-->
END%% END%%
@ -558,7 +562,7 @@ END%%
%%ANKI %%ANKI
Basic Basic
When is a floating-point number considered denormalized? When is a floating-point number considered denormalized?
Back: When the exponent field is either all `0`s or all `1`s. Back: When the exponent field is all `0`s.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710556915061--> <!--ID: 1710556915061-->
END%% END%%
@ -953,6 +957,503 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
<!--ID: 1710605798354--> <!--ID: 1710605798354-->
END%% END%%
%%ANKI
Basic
What three forms can an IEEE floating-point number take on?
Back: Normalized, denormalized, and special value.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710672470749-->
END%%
%%ANKI
Basic
When is a floating-point number considered a special value?
Back: When the exponent field is all `1`s.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710672470791-->
END%%
%%ANKI
Basic
What special values can a floating-point number take on?
Back: $\infty$ and $NaN$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710672470794-->
END%%
%%ANKI
Basic
Representable floating-point numbers are denser around what?
Back: $0$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710672470797-->
END%%
%%ANKI
Basic
IEEE floating-point was designed to allow efficiently sorting using what?
Back: An integer sorting routine.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710672470799-->
END%%
%%ANKI
Basic
*Why* can IEEE floating-point values be sorted using an integer sorting routine?
Back: The unsigned interpretation of ascending floating-point numbers is also ascending.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710672470801-->
END%%
%%ANKI
Basic
What complication exists in integer sorting routines applied to IEEE floating-point values?
Back: The unsigned interpretation of negative floating-point numbers is in descending order.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710672470805-->
END%%
## Rounding
Because floating-point arithmetic can't represent every real number, it must round results to the "nearest" representable number, however "nearest" is defined. The IEEE floating-point standard defines four **rounding modes** to influence this behavior:
* **Round-to-even** rounds numbers to the closest representable value. In the case of values equally between two representations, it rounds to the number with an even least significant digit.
* **Round-toward-zero** rounds downward for positive values and upward for negative values.
* **Round-down** always rounds downward.
* **Round-up** always rounds upward.
%%ANKI
Basic
What are the four rounding modes supported in the IEEE floating-point standard?
Back: Round-to-even, round-toward-zero, round-down, and round-up.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824748-->
END%%
%%ANKI
Cloze
{1:Round-toward-zero} is to {2:integer} division whereas {2:round-down} is to {1:floor} division.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824750-->
END%%
%%ANKI
Cloze
{1:Round-up} is to {2:ceiling} division whereas {2:round-toward-zero} is to {1:integer} division.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824752-->
END%%
%%ANKI
Basic
What is the default IEEE floating-point standard rounding mode?
Back: Round-to-even.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824754-->
END%%
%%ANKI
Basic
What alternative name does round-to-even go by?
Back: Round-to-nearest.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824757-->
END%%
%%ANKI
Basic
How is floating-point `1.40` rounded in round-to-even mode?
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: 1710680824759-->
END%%
%%ANKI
Basic
How is floating-point `1.50` rounded in round-to-even mode?
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: 1710680824761-->
END%%
%%ANKI
Basic
How is floating-point `1.60` rounded in round-to-even mode?
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: 1710680824763-->
END%%
%%ANKI
Basic
How is floating-point `-1.50` rounded in round-to-even mode?
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: 1710680824765-->
END%%
%%ANKI
Basic
How is floating-point `1.40` rounded in round-to-zero mode?
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: 1710680824767-->
END%%
%%ANKI
Basic
How is floating-point `1.50` rounded in round-to-zero mode?
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: 1710680824769-->
END%%
%%ANKI
Basic
How is floating-point `-1.50` rounded in round-to-zero mode?
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: 1710680824771-->
END%%
%%ANKI
Basic
How is floating-point `1.40` rounded in round-down mode?
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: 1710680824774-->
END%%
%%ANKI
Basic
How is floating-point `1.50` rounded in round-down mode?
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: 1710680824776-->
END%%
%%ANKI
Basic
How is floating-point `-1.50` rounded in round-down mode?
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: 1710680824778-->
END%%
%%ANKI
Basic
How is floating-point `1.40` rounded in round-up mode?
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: 1710680824780-->
END%%
%%ANKI
Basic
How is floating-point `1.50` rounded in round-up mode?
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: 1710680824782-->
END%%
%%ANKI
Basic
How is floating-point `-1.50` rounded in round-up mode?
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: 1710680824785-->
END%%
%%ANKI
Basic
*Why* does round-to-even prefer even over odd numbers?
Back: This is an arbitrary choice.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824787-->
END%%
%%ANKI
Basic
*Why* does round-to-even prefer even over always rounding down?
Back: The former more reliably avoids potential statistical biases.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824790-->
END%%
%%ANKI
Basic
In round-to-even rounding, what bit is considered even?
Back: `0`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824792-->
END%%
%%ANKI
Basic
In round-to-even rounding, what bit is considered odd?
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: 1710680824794-->
END%%
%%ANKI
Basic
How does the IEEE floating-point standard define $1/-0$?
Back: $-\infty$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824796-->
END%%
%%ANKI
Basic
How does the IEEE floating-point standard define $1/+0$?
Back: $\infty$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824798-->
END%%
%%ANKI
Basic
What value(s) do IEEE floating-point numbers take on in the case of overflow?
Back: $\pm\infty$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824800-->
END%%
%%ANKI
Basic
What value(s) do IEEE floating-point numbers take on in the case of underflow?
Back: $0$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824802-->
END%%
## Arithmetic
%%ANKI
Basic
What does $+^f$ denote?
Back: Floating-point addition.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824805-->
END%%
%%ANKI
Basic
What is the result of $x +^f y$?
Back: $Round(x + y)$ where $Round$ refers to the current rounding-mode.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824808-->
END%%
%%ANKI
Basic
Is $+^f$ commutative?
Back: Yes.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824810-->
END%%
%%ANKI
Basic
Is $+^f$ associative?
Back: No.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824813-->
END%%
%%ANKI
Basic
Which IEEE floating-point values do not have an additive inverse?
Back: $\pm\infty$ and $NaN$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824815-->
END%%
%%ANKI
Basic
Let $f$ be a normalized floating-point value. What is its additive inverse?
Back: $-f$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824817-->
END%%
%%ANKI
Basic
Let $f$ be a denormalized floating-point value. What is its additive inverse?
Back: $-f$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824819-->
END%%
%%ANKI
Basic
Let $f$ be a special floating-point value. What is its additive inverse?
Back: N/A
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824822-->
END%%
%%ANKI
Basic
What is the most important group quality $+^f$ is lacking?
Back: Associativity.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824824-->
END%%
%%ANKI
Basic
What does $*^f$ denote?
Back: Floating-point multiplication.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824826-->
END%%
%%ANKI
Basic
What is the result of $x *^f* y$?
Back: $Round(x * y)$ where $Round$ refers to the current rounding-mode.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824827-->
END%%
%%ANKI
Basic
Is $*^f$ commutative?
Back: Yes.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824829-->
END%%
%%ANKI
Basic
Is $*^f$ associative?
Back: No.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824832-->
END%%
%%ANKI
Basic
What is the multiplicative identity of $*^f$?
Back: $1.0$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824834-->
END%%
%%ANKI
Basic
Does $*^f$ distribute over $+^f$?
Back: No.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824836-->
END%%
%%ANKI
Basic
What property of floating-point values prevents it behaving like "real math"?
Back: It represents a finite number of values and rounds results if need be.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824838-->
END%%
%%ANKI
Basic
How is precision affected when casting from `float` to `double`?
Back: It isn't.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824841-->
END%%
%%ANKI
Basic
How is precision affected when casting from `double` to `float`?
Back: Rounding may occur.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824844-->
END%%
%%ANKI
Basic
*Why* might rounding occur when casting from `double` to `float`?
Back: `float`s have less precision.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824846-->
END%%
%%ANKI
Basic
What overflow values might result when casting from `float` to `double`?
Back: N/A
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824848-->
END%%
%%ANKI
Basic
What overflow values might result when casting from `double` to `float`?
Back: $\pm\infty$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824850-->
END%%
%%ANKI
Basic
*Why* might overflow occur when casting from `double` to `float`?
Back: `float`s have smaller range.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824852-->
END%%
%%ANKI
Basic
Assuming no overflow, what is the result of casting a `double` to an `int`?
Back: The `double`'s value rounded toward `0`.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824856-->
END%%
%%ANKI
Basic
Assuming overflow, what is the result of casting a `double` to an `int`?
Back: The result is implementation-specific.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824858-->
END%%
%%ANKI
Basic
Assuming no overflow, what is the result of casting a `float` to an `int`?
Back: The `float`'s value rounded toward `0`.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824861-->
END%%
%%ANKI
Basic
What is the result of `(int) (double) 1.5`?
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: 1710680824863-->
END%%
%%ANKI
Basic
What is the result of `(int) (double) -1.5`?
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: 1710680824865-->
END%%
%%ANKI
Basic
Assuming overflow, what is the result of casting a `float` to an `int`?
Back: The result is implementation-specific.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824867-->
END%%
## References ## References
* 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.

86
notes/encoding/integer.md
View File

@ -1,5 +1,5 @@
--- ---
title: Integer Encoding title: Integers
TARGET DECK: Obsidian::STEM TARGET DECK: Obsidian::STEM
FILE TAGS: binary::integer FILE TAGS: binary::integer
tags: tags:
@ -230,7 +230,7 @@ END%%
%%ANKI %%ANKI
Basic Basic
How does Bryant et al. define $B2U_w$? How does Bryant et al. define $B2U_w$?
Back: $B2U_w(\vec{x}) = 2^{w-1}x_{w-1} + \sum_{i=0}^{w-2} 2^ix_i$ Back: $B2U_w(\vec{x}) = 2^{w-1}x_{w-1} + \sum_{k=0}^{w-2} 2^kx_k$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1708179147785--> <!--ID: 1708179147785-->
END%% END%%
@ -415,7 +415,7 @@ END%%
%%ANKI %%ANKI
Basic Basic
How does Bryant et al. define $B2T_w$? How does Bryant et al. define $B2T_w$?
Back: $B2T_w(\vec{x}) = -2^{w-1}x_{w-1} + \sum_{i=0}^{w-2} 2^ix_i$ Back: $B2T_w(\vec{x}) = -2^{w-1}x_{w-1} + \sum_{k=0}^{w-2} 2^kx_k$
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1708179649901--> <!--ID: 1708179649901-->
END%% END%%
@ -1138,6 +1138,22 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
<!--ID: 1709492205964--> <!--ID: 1709492205964-->
END%% END%%
%%ANKI
Basic
Is $+_w^u$ commutative?
Back: Yes.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824725-->
END%%
%%ANKI
Basic
Is $+_w^u$ associative?
Back: Yes.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824728-->
END%%
Two's-complement addition, denoted $+_w^t$ operates similarly: Two's-complement addition, denoted $+_w^t$ operates similarly:
$$x +_w^u y = \begin{cases} $$x +_w^u y = \begin{cases}
@ -1361,6 +1377,22 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
<!--ID: 1709492205974--> <!--ID: 1709492205974-->
END%% END%%
%%ANKI
Basic
Is $+_w^t$ commutative?
Back: Yes.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824730-->
END%%
%%ANKI
Basic
Is $+_w^t$ associative?
Back: Yes.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824733-->
END%%
### Shifting ### Shifting
Left shift operations (`<<`) drop the `k` most significant bits and fills the right end of the result with `k` zeros. Right shift operations (`>>`) are classified in two ways: Left shift operations (`<<`) drop the `k` most significant bits and fills the right end of the result with `k` zeros. Right shift operations (`>>`) are classified in two ways:
@ -1677,6 +1709,30 @@ Tags: c17
<!--ID: 1709831032382--> <!--ID: 1709831032382-->
END%% END%%
%%ANKI
Basic
Is $*_w^u$ commutative?
Back: Yes.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824735-->
END%%
%%ANKI
Basic
Is $*_w^u$ associative?
Back: Yes.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824737-->
END%%
%%ANKI
Basic
Does $*^u_w$ distribute over $+^u_w$?
Back: Yes.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824740-->
END%%
Similarly, two's-complement multiplication is defined as follows: $$x *_w^t y = U2T_w((x \cdot y) \bmod 2^w)$$ Similarly, two's-complement multiplication is defined as follows: $$x *_w^t y = U2T_w((x \cdot y) \bmod 2^w)$$
%%ANKI %%ANKI
@ -1815,6 +1871,30 @@ Tags: c17
<!--ID: 1709831032386--> <!--ID: 1709831032386-->
END%% END%%
%%ANKI
Basic
Is $*_w^t$ commutative?
Back: Yes.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824742-->
END%%
%%ANKI
Basic
Is $*_w^t$ associative?
Back: Yes.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824744-->
END%%
%%ANKI
Basic
Does $*^t_w$ distribute over $+^t_w$?
Back: Yes.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1710680824746-->
END%%
%%ANKI %%ANKI
Basic Basic
How can we rewrite $x \cdot 1101_2$ as an expression of *only* `<<` and `+`? How can we rewrite $x \cdot 1101_2$ as an expression of *only* `<<` and `+`?