diff options
| author | Marvin Borner | 2024-04-25 16:18:21 +0200 |
|---|---|---|
| committer | Marvin Borner | 2024-04-25 16:18:21 +0200 |
| commit | 3fb29797cb2251e868bbd16918117b68962faaa8 (patch) | |
| tree | 36e5c51c97da028e521bc4a0ce69bf4d1b19a9a4 /std/Math/Real.bruijn | |
| parent | 2ac808e5ac77a84166973691b2a1e4e0afa9a308 (diff) | |
Various experiments
Diffstat (limited to 'std/Math/Real.bruijn')
| -rw-r--r-- | std/Math/Real.bruijn | 38 |
1 files changed, 28 insertions, 10 deletions
diff --git a/std/Math/Real.bruijn b/std/Math/Real.bruijn index 437a947..59a32e3 100644 --- a/std/Math/Real.bruijn +++ b/std/Math/Real.bruijn @@ -79,39 +79,57 @@ compress b Q.compress ⧗ Real → Real # --- -:import std/List . +:import std/List L # ∑(1/n^2) # converges to 1.6449... -frac-1/n² [^(0 &[[(Q.add 1 op) : N.++0]] start)] ⧗ Real +unary-1/n² [0 &[[(Q.add 1 op) : N.++0]] start [[0]]] ⧗ Real op (+1) : N.--(N.mul 0 0) start (+0.0f) : (+1) # ∑(x^n/n!) = e^x # inefficient Taylor expansion -frac-slow-exp [[^(0 &[[(Q.add 1 op) : N.++0]] start)]] ⧗ Number → Real +unary-slow-exp [[0 &[[(Q.add 1 op) : N.++0]] start [[0]]]] ⧗ Number → Real op (N.pow 3 0) : N.--(N.fac 0) start (+0.0f) : (+1) # ∑(x^n/n!) = e^x # more efficient Taylor expansion -frac-exp [[(0 &[[[[[[[2 1 0 (Q.add 4 op) N.++3]] pow fac]]]]] start) [[[[1]]]]]] ⧗ Number → Real +unary-exp [[0 &[[[[[[[2 1 0 (Q.add 4 op) N.++3]] pow fac]]]]] start [[[[1]]]]]] ⧗ Number → Real pow N.mul 6 4 fac N.mul 1 3 op 1 : N.--0 start [0 (+1) (+1) (+1.0f) (+1)] +# equivalent to unary-exp but with ternary index using infinite list iteration +iter-exp [0 [[[[1]]]]] ∘∘ [L.…!!… (L.iterate &[[[[op]]]] start)] ⧗ Number → Real + start [0 (+1) (+1) (+1.0f) (+1)] + op [[[2 1 0 (Q.add 4 (1 : N.--0)) N.++3]] pow fac] + pow N.mul 5 4 + fac N.mul 1 3 + # real^number -pow-n […!!… (iterate (mul 0) (+1.0r))] ⧗ Real → Number → Real +pow-n [L.…!!… (L.iterate (mul 0) (+1.0r))] ⧗ Real → Number → Real + +lim-exp [[pow-n [(N.add 2 1) : N.--1] 0]] + +iter-slow-ln [0 [[[[1]]]]] ∘∘ [L.…!!… (L.iterate &[[[[op]]]] start)] ⧗ Number → Real + start [0 (+1) (+1) (+0.0f) (+0)] + op [[[2 1 0 (Q.add 4 go) N.++3]] 4 3] + go Q.mul l r + l (+2) : (N.mul (+2) 3) + r Q.pow-n (N.--7 : 7) N.++(N.mul (+2) 3) -exp [y [[[[rec]]]] (+1) (+1.0r) (+1.0r)] - rec (1 / 0) + (3 N.++2 (1 ⋅ 4) (0 ⋅ (number→real 2))) +iter-ln [0 [[[1]]]] ∘∘ [L.…!!… (L.iterate &[[[op]]] start)] ⧗ Number → Real + start [0 (N.--1 : 1) (+0.0f) (+0)] + op [0 pow (Q.add 2 go) N.++1] + pow Q.mul 3 (Q.pow-n (N.--4 : 4) (+2)) + go Q.mul ((+2) : (N.mul (+2) 1)) 3 -ln [y [[[rec]]] (+1) 0] - rec (N.=²?1 -‣ [0] (0 / (number→real 1))) + (2 N.++1 (3 ⋅ 0)) +derive [[[[((3 (0 + 1)) - (3 0)) / 1]] [(+1) : 1] 0]] ⧗ (Real → Real) → (Real → Real) # power function -pow [[exp (0 ⋅ (ln 1))]] ⧗ Real → Real → Real +pow [[iter-exp (0 ⋅ (iter-ln 1))]] ⧗ Real → Real → Real …**… pow |