Enhance the precision of fixed-point square root computations #16

marvin0102 · 2024-07-24T13:18:11Z

The original fixed point sqrt can not calculate sqrt of numbers less than 1. Implement a new sqrt calculation that is more precise and without fixed point multiplication.
Below is the comparison of sqrt from 0~2. "math.h" stands for function 'sqrt()' from library math.h. "original" stands for original sqrt implementation. "precise" stands for new implemented method.

src/fixed.c

src/image-jpeg.c

src/fixed.c

jserv

Rebase the latest main branch to enable CI pipeline.

jserv

Improve the git commit messages by using complete sentences and making them informative.

src/fixed.c

jserv · 2024-07-25T13:57:52Z

You should avoid submitting pull requests via the main branch (or default branch). Instead, always create a dedicated git branch to work on specific features or bug fixes.

In this case, you should perform the following steps to resolve the unintended conflicts:

$ git remote add upstream https://github.com/sysprog21/mado
$ git fetch upstream
$ git reset --hard 65fa6e742a6bc16b31b6b41d3dec722857298a7f
$ git cherry-pick origin/main
$ git rebase upstream/main

After verifying via git log, do git push --force.

Improve your skills with Git by watching the videos: https://hackmd.io/@sysprog/git-with-github

src/fixed.c

weihsinyeh · 2024-07-25T17:02:38Z

src/fixed.c

+    if (as <= 0)
+        return 0;
+    if (CHECK_INTERVAL(as, TWIN_SFIXED_ONE, (1 << (2 - 1))))
+        return TWIN_SFIXED_ONE;


I'm curious about the reason for using CHECK_INTERVAL.

The following figure is the implementation without the CHECK_INTERVAL.

This method is used to find an approximation of sin and cos values. However, this method makes it hard to calculate the square root when the numbers are near 1, which causes the wrong approximation of sin and cos values, especially when the radian is near pi/2 or 0.

The two figures below are sin and cos value calculted with (first) and without (second) CHECK_INTERVAL. Test on rv32emu/tests/line.c.

src/fixed.c

The current square root calculation for fixed-point numbers cannot handle values less than 1 accurately. To improve precision, replace the existing method with the digit-by-digit calculation method. This approach, combined with offset manipulation, will minimize precision loss during the square root calculation.

jserv · 2024-07-26T12:07:20Z

Thank @marvin0102 for contributing!

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jserv changed the title ~~Implement precise square root calculation for fixed point~~ Enhance the precision of fixed-point square root computations Jul 24, 2024

jserv requested a review from weihsinyeh July 24, 2024 13:28

jserv reviewed Jul 24, 2024

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