🏛️ Diophantine    

$ go run github.com/teal-finance/diophantine/cmd@latest -list 0.770507 -farey

Approximated fractions using the Farey series by Bodo
#0     770507 / 1000000     0
#1     267641 / 347357      3e-12
#2     235225 / 305286      7e-12
#3      32416 / 42071       7e-11
#4       8313 / 10789       2e-09
#5       7477 / 9704        7e-09
#6        836 / 1085        9e-08
#7        789 / 1024        8e-07 Denominator is power of two
#8         47 / 61          2e-05
#9         37 / 48          0.0003
#10        10 / 13          0.001
#11         7 / 9           0.007

Diophantine is a pure Go lib and CLI to approximate a floatting number (0.770507) by a fraction of two integers (e.g. 7/9), also known as rational approximation, fraction approximation or ratio approximation. Diophantine use the functions of two other projects:

• github.com/bodokaiser/approx
• github.com/pnelson/fraction

The name is from the Diophantine approximation named after Diophantus of Alexandria, a mathematician in the Roman Empire, who was the author of books called Arithmetica. Diophantus was the first Greek mathematician who recognized fractions as numbers. His books have been translated to Arabic during the Islamic Golden Age, then translated to Latin during the Renaissance.

🧑‍💻 CLI

$ go run github.com/teal-finance/diophantine/cmd@latest -list 0.770507 -farey -phil

Approximated fractions using the Farey series by Bodo
#0     770507 / 1000000     0
#1     267641 / 347357      3e-12
#2     235225 / 305286      7e-12
#3      32416 / 42071       7e-11
#4       8313 / 10789       2e-09
#5       7477 / 9704        7e-09
#6        836 / 1085        9e-08
#7        789 / 1024        8e-07 Denominator is power of two
#8         47 / 61          2e-05
#9         37 / 48          0.0003
#10        10 / 13          0.001
#11         7 / 9           0.007

Approximated fractions using the Phil's implementation
#0     770507 / 1000000     0
#1     267641 / 347357      3e-12
#2     235225 / 305286      7e-12
#3      32416 / 42071       7e-11
#4       8313 / 10789       2e-09
#5       7477 / 9704        7e-09
#6        836 / 1085        9e-08
#7        789 / 1024        8e-07 Denominator is power of two
#8         47 / 61          2e-05
#9         37 / 48          0.0003
#10        10 / 13          0.001
#11         7 / 9           0.007

📚 Library

Diophantine can also be used as a library.

See https://pkg.go.dev/github.com/teal-finance/diophantine.

🛠️ Alternative tools

Some online tools to approximate fractions:

• https://oss.sheetjs.com/frac/
• https://www.johndcook.com/rational_approximation.html

✨ Contributions Welcome

This new project needs your help to become better. Please propose your enhancements, or even a further refactoring.

We welcome contributions in many forms, and there's always plenty to do!

🗣️ Feedback

If you have some suggestions, or need a new feature, please contact us:

• issues tracking
• e-mail at Teal.Finance(à)pm.me
• Twitter at @TealFinance

Feel free to propose a Pull Request, your contributions are welcome. 😉

🗽 Copyright and license

Copyright (c) 2022 Teal.Finance contributors

Diophantine is free software, and can be redistributed and/or modified under the terms of the MIT License. SPDX-License-Identifier: MIT

Diophantine is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

See the LICENSE file (alongside the source files) or https://opensource.org/licenses/MIT.