https://github.com/githubharald/fast_inv_sqrt
Fast approximation of the inverse square root 1/√(x).
https://github.com/githubharald/fast_inv_sqrt
Last synced: about 2 months ago
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Fast approximation of the inverse square root 1/√(x).
- Host: GitHub
- URL: https://github.com/githubharald/fast_inv_sqrt
- Owner: githubharald
- Created: 2020-10-29T21:18:08.000Z (over 4 years ago)
- Default Branch: master
- Last Pushed: 2020-10-31T13:27:48.000Z (over 4 years ago)
- Last Synced: 2025-01-20T06:13:48.378Z (3 months ago)
- Language: C++
- Homepage: https://githubharald.github.io/fast_inv_sqrt.html
- Size: 38.1 KB
- Stars: 2
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Fast Inverse Square Root
This repository implements a fast approximation of the inverse square root: 1/√(x).
It is a simplified version of the famous hack used in the 3D game Quake in the 90s.
## Get started
### Code snippet
If you just need the code, simply copy and paste the following code snippet.
````cpp
#include
#include
float fast_inv_sqrt(float x)
{
float y = x; // y holds the current guess for 1/sqrt(x)
uint32_t *i = reinterpret_cast(&y); // i points to current guess y
const uint32_t exp_mask = 0x7F800000; // 0xFF<<23
const uint32_t magic_number = 0x5f000000; // 190<<23
// initial guess using magic number
*i = magic_number - ((*i >> 1) & exp_mask);
// refine guess using small number of Newton iterations
const size_t num_newton_iter = 2;
for (size_t i = 0; i < num_newton_iter; ++i)
{
y = (x * y * y + 1) / (2 * x * y);
}
return y;
}
````
### Analyze algorithm
* Go to `src/`
* Compile the C++ code, e.g. `g++ -O2 fast_inv_sqrt.cpp`, this creates a binary
* Execute the binary, which produces a file "dump.csv"
* Execute the Python script, e.g. `python3 analyze.py`, this shows the plots
## Error
The algorithm performs two steps:
* Apply "bit-magic" to compute an initial guess with at most 41% relative error
* Apply 2 iterations of Newton's method to drive the maximum relative error down to <0.2%
The plot shows the relative error after each of the two steps for x values from 1 to 16.
For more details see [this article](https://githubharald.github.io/fast_inv_sqrt.html).
