Lines Matching +full:root +full:- +full:mean +full:- +full:square

28 is faster than Karatsuba. There is a script (`$ROOT/scripts/karatsuba.py`) that
61 ### Square Root
64 Newton-Raphson Method, or the [Babylonian Method][5]) to perform the square root
75 x - x^3/3! + x^5/5! - x^7/7! + ...
124 (where `a` is equal to `(x - 1)/(x + 1)`) to calculate `ln(x)` when `x` is small
144 x - x^3/3 + x^5/5 - x^7/7 + ...
150 atan(x) = atan(c) + atan((x - c)/(1 + x * c))
164 x^n/(2^n * n!) * (1 - x^2 * 2 * 1! * (n + 1)) + x^4/(2^4 * 2! * (n + 1) * (n + 2)) - ...
172 j(-n,x) = (-1)^n * j(n,x)
183 This `dc` uses the [Memory-efficient method][8] to compute modular
188 ### Non-Integer Exponentiation (`bc` Math Library 2 Only)
211 `z` is set to zero as a flag and as a value. What I mean by that will be clear
216 if it was an integer). We also save the number in `z`; being non-zero is a flag
221 relationship `l(x) == -l(1/x)`; we negated the exponent, which is equivalent to
252 calculate `e((y - a) * l(x))`, where `a` is the integer portion of `y`. It's
253 easy to see that `y - a` will be just the fractional portion of `y` (the
294 The algorithm is to use the formula `n!/(n-k)!`.
302 The algorithm is to use the formula `n!/r!*(n-r)!`.
328 ### Root (`bc` Math Library 2 Only)
330 This is implemented in the function `root(x,n)`.
335 Like square root, its complexity is `O(log(n)*n^2)` as it requires one division
338 ### Cube Root (`bc` Math Library 2 Only)
342 This is a convenience wrapper around `root(x,3)`.
394 [8]: https://en.wikipedia.org/wiki/Modular_exponentiation#Memory-efficient_method
395 [9]: https://en.wikipedia.org/wiki/Root-finding_algorithms#Newton's_method_(and_similar_derivative-…