$ 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:
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.
$ 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
Diophantine can also be used as a library.
See https://pkg.go.dev/github.com/teal-finance/diophantine.
Some online tools to approximate fractions:
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!
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 (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.