mirror of
https://github.com/pkivolowitz/asm_book.git
synced 2026-06-21 07:06:47 +08:00
89 lines
2.9 KiB
Markdown
89 lines
2.9 KiB
Markdown
# Section 2 / Floating Point
|
|
|
|
This chapter deals exclusively with the handling of floating point
|
|
operations on the AARCH64 platform.
|
|
|
|
## What are Floating Point Numbers?
|
|
|
|
Let's first begin with an understanding of what floating point numbers
|
|
are. [That can be found here](./what.md).
|
|
|
|
The TL;DR is that floating point numbers are approximations with double
|
|
precision being better approximations that single precision.
|
|
|
|
Floating point numbers have a sign bit (for signed floating points), an
|
|
exponent which controls the range of representable numbers, and a
|
|
mantissa that controls precision.
|
|
|
|
## Floating Point Registers
|
|
|
|
There are 31 general registers (the X and W registers). Similarly there
|
|
are 31 floating point registers which are reused for single, double and
|
|
vector (SIMD - Single Instruction Multiple Data) instructions.
|
|
|
|
A bit more detail [is provided here](./working.md).
|
|
|
|
## Rounding and Truncation
|
|
|
|
Truncation is part of casting `float` and `double` to `int` and `long`.
|
|
|
|
Rounding is important too.
|
|
|
|
[Coverage on rounding and truncation is found here](./rounding.md).
|
|
|
|
## Loading Floating Point Numbers into Registers
|
|
|
|
This is a little confusing because some values can be loaded from
|
|
arguments in the `fmov` instruction. For example, 1.0 can be `fmov`ed.
|
|
Trying to do the same for 1.1 will fail. Remember that AARCH64
|
|
instructions are always 32 bits wide and that floating point numbers are
|
|
at least that size.
|
|
|
|
[This chapter](./literals.md) covers the loading of floating numbers
|
|
into registers. A sample program is linked below.
|
|
|
|
## Nuances of `fmov`
|
|
|
|
As indicated above, you can `fmov` a floating point literal into a
|
|
register. Except when you can't. Well, mostly you can't.
|
|
|
|
Additionally, there are some rules about using `fmov` between registers.
|
|
|
|
[This chapter](../../not_written_yet.md) covers the nuances of using
|
|
`fmov`.
|
|
|
|
## Half Precision Floating Point Numbers
|
|
|
|
Often used in Computer Graphics, half precision floats fit within 16
|
|
bits, the size of a `short`.
|
|
|
|
The TL;DR here is: Avoid them.
|
|
|
|
[This chapter explains why](./half.md).
|
|
|
|
## SIMD
|
|
|
|
There are two types of SIMD instruction sets available in the AARCH64
|
|
ISA but the makers of processors are not obligated to implement them on
|
|
any particular chip.
|
|
|
|
The first kind is NEON.
|
|
[This is described here.](./../../not_written_yet.md)
|
|
|
|
The second kind of Scalable Vector Extension (SVE) for which we do not
|
|
have near-term plans to cover.
|
|
|
|
## Demo Programs in this Chapter
|
|
|
|
In case you want to get right to the code, here are the demos presented
|
|
in this chapter.
|
|
|
|
If you receive the assembly language files with a lower case extension,
|
|
you will need to make the `.s` extension into `.S`.
|
|
|
|
| Link | Contents | Converged |
|
|
| ---- | -------- | --------- |
|
|
| [Link](./float_dump.cpp) | Deconstructs floating point values | NA |
|
|
| [Link](./asm_rounding.S) | Demonstrates some rounding in asm | Yes |
|
|
| [Link](./rounding.cpp) | Demonstrates some rounding in C++ | NA |
|
|
| [Link](./literals.S) | Demonstrates dealing with floating point literals | Yes |
|