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Diffstat (limited to 'std/Math/Real.bruijn')
| -rw-r--r-- | std/Math/Real.bruijn | 18 |
1 files changed, 18 insertions, 0 deletions
diff --git a/std/Math/Real.bruijn b/std/Math/Real.bruijn index 4b3e7d0..9a4b1bd 100644 --- a/std/Math/Real.bruijn +++ b/std/Math/Real.bruijn @@ -139,6 +139,12 @@ sqrt [[y [[[N.=?0 guess go]]] (1 0) 0]] ⧗ Real → Real guess (+1.0q) go [Q.div (Q.add 0 (Q.div 2 0)) (+2.0q)] (2 1 N.--0) +# Newton's/Heron's method, quadratic convergence +# tex: x_{n+1}=\frac{3x_n+a/(x_n^2)}{4} +cbrt [[y [[[N.=?0 guess go]]] (1 0) 0]] ⧗ Real → Real + guess (+1.0q) + go [Q.div (Q.add (Q.mul (+3.0q) 0) (Q.div 2 (Q.mul 0 0))) (+4.0q)] (2 1 N.--0) + # hypotenuse hypot [[sqrt ((0 ⋅ 0) + (1 ⋅ 1))]] ⧗ Real → Real → Real @@ -164,6 +170,18 @@ hypot [[sqrt ((0 ⋅ 0) + (1 ⋅ 1))]] ⧗ Real → Real → Real p Q.mul (+2.0q) 2 final [[[[Q.div (Q.pow-n (Q.add 3 2) (+2)) (Q.mul (+4.0q) 1)]]]] +# golden ratio from direct formula +φ ++(sqrt (+5.0r)) / (+2.0r) + +# conjugate golden ratio +ψ -(~φ) + +# golden ratio from fibonacci convergence +φ* [(L.index (L.iterate &[[0 : (N.add 1 0)]] ((+0) : (+1))) 0) [[1 : N.--0]]] + +# real fibonacci +fib [((pow φ 0) - (pow ψ 0)) / (sqrt (+5.0r))] + # 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 |