bigdecimal
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ruby
Implement BigMath::PI with Gauss-Legendre algorithm
It's fast and simple.
Pi calculation will be the bottleneck when we improve sin/cos or erf/erfc with bit burst algorithm.
Multiplication cost needs to be less than O(N^2). Requires #407.
Time and error. PI(prec) calculates prec+16 digits internally and round to prec digits.
| calculation | time | correct_digits | last 5 digits of extra 16 digits |
|---|---|---|---|
| PI(1000000) | 9.171798s | 1000015 | calculated: 20849 true_value: 20845 |
| PI(10000000) | 135.526677s | 10000015 | calculated: 26483 true_value: 26482 |
| PI(100000000) | 1624.233964s | 100000014 | calculated: 78333 true_value: 78327 |
