pihex

Arbitrary place hexadecimal digits viewer of pi written in Rust. The library is based on the Bailey-Borwein-Plouffe formula (BBP formula) and Bellard's formula.

 $ pihex
0: 243f 6a88 85a3 08d3 1319 8a2e 0370 7344
 $ pihex 1
2: 3f6a 8885 a308 d313 198a 2e03 7073 44a4
 $ pihex 4
4: 6a88 85a3 08d3 1319 8a2e 0370 7344 a409
 $ pihex 8
128: 9216 d5d9 8979 fb1b d131 0ba6 98df b5ac
 $ pihex 65536
65536: 3004 3414 c926 7212 d7fb 8a3f fc7c 7002
 $ pihex 1000000
1000000: 6c65 e52c b459 3500 50e4 bb17 8f4c 67a0
 $ pihex 10000000
10000000: 7af5 863e fed8 de97 033c d0f6 b80a 3d26
 $ pihex 100000000 # defaults to BBP formula
100000000: cb84 0e21 926e c5ae 0d2f 3405 1045 93cb
 $ pihex --formula=bellard 100000000 # yields the same result but faster than BBP formula
100000000: cb84 0e21 926e c5ae 0d2f 3405 1045 93cb

Refer to pihex --help for further details.

Installation

Homebrew

brew install itchyny/tap/pihex

Build from crates.io

cargo install pihex

Build from source

git clone https://github.com/itchyny/pihex
cd pihex
cargo install --path .

Author

itchyny (https://github.com/itchyny)

License

This software is released under the MIT License, see LICENSE.

Disclaimer

I tested very carefully but this software does not always answer correctly due to the floating-point arithmetic inaccuracy. If there's a place with over 53bit zeros in binary representation of pi (I'm not sure where it is), we never ensure the answer calculated by double-precision floating-point numbers is correct. Therefore when you use this software, be careful the answer is not suffered from floating-point calculation errors. If the successive digits in hexadecimal representation repeat '0' or 'f' over 13 times, it's highly inaccurate due to this calculation errors.

References

• David H. Bailey, Peter Borwein, and Simon Plouffe, On the Rapid Computation of Various Polylogarithmic Constants, Mathematics of Computation 66, 903-913, 1997.
• David H. Bailey, The BBP Algorithm for Pi, September 17, 2006.
• Fabrice Bellard, A new formula to compute the n'th binary digit of pi, 1997.