diff options
| author | Marvin Borner | 2024-05-17 13:33:53 +0200 |
|---|---|---|
| committer | Marvin Borner | 2024-05-17 13:33:53 +0200 |
| commit | 8044eb95639d96512c8891b0c4dca11a4e9e162a (patch) | |
| tree | 7f8ed69f92babf4cd9903b2dcac4ed68a8f6a3f6 /std/Math/Real.bruijn | |
| parent | 99ec17a582ce40c35e9be76415b3a4a6dcff65ae (diff) | |
Minor additions :)
Diffstat (limited to 'std/Math/Real.bruijn')
| -rw-r--r-- | std/Math/Real.bruijn | 12 |
1 files changed, 11 insertions, 1 deletions
diff --git a/std/Math/Real.bruijn b/std/Math/Real.bruijn index 28bc512..4b3e7d0 100644 --- a/std/Math/Real.bruijn +++ b/std/Math/Real.bruijn @@ -151,9 +151,19 @@ hypot [[sqrt ((0 ⋅ 0) + (1 ⋅ 1))]] ⧗ Real → Real → Real denom [N.mul 2 (N.mul 0 N.++0)] (N.mul (+2) 5) # ratio of circle's circumference to its diameter -# TODO: Gauss-Legendre π π/2 ⋅ (+2.0r) ⧗ Real +# Gauss-Legendre, quadratic convergence +# Chudnovsky would be even faster but is ugly (i.e. magic numbers) +π-gauss [L.nth-iterate &[[[[op]]]] start 0 final] + start [0 (+1.0q) Q.~(sqrt (+2.0r) 1) (+0.25q) (+1.0q)] + op [[1 0 b t p] a] + a Q.div (Q.add 4 3) (+2.0q) + b sqrt [Q.mul 6 5] 6 + t Q.sub 3 (Q.mul 2 (Q.pow-n (Q.sub 5 0) (+2))) + p Q.mul (+2.0q) 2 + final [[[[Q.div (Q.pow-n (Q.add 3 2) (+2)) (Q.mul (+4.0q) 1)]]]] + # arctan by Taylor expansion, only for |x|<=1 # tex: \sum_{n=0}^\infty(-1)^n \frac{x^{2n+1}}{2n+1} arctan* [[[L.nth-iterate &[[[[op]]]] start 1] (1 0) [[[[3]]]]]] ⧗ Real → Real |