blob: 156e1c8e90a0a4adf72f6350d4fc0fbbfeadfc53 (
plain) (
blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
|
# MIT License, Copyright (c) 2022 Marvin Borner
:input std/Number
:import std/List .
# adds all values in list
sum foldl add (+0) ⧗ (List Number) → Number
∑‣ sum
:test (∑((+1) : ((+2) : {}(+3)))) ((+6))
# returns max value of list
lmax foldl1 max ⧗ (List Number) → Number
:test (lmax ((+1) : ((+3) : {}(+2)))) ((+3))
# returns min value of list
lmin foldl1 min ⧗ (List Number) → Number
:test (lmin ((+2) : ((+1) : {}(+0)))) ((+0))
# list from num to num
{…→…} z [[[rec]]] ⧗ Number → Number → (List Number)
rec (1 =? ++0) case-end case-list
case-list 1 : (2 ++1 0)
case-end empty
:test ({ (+0) → (+2) }) ((+0) : ((+1) : {}(+2)))
# equivalent of mathematical sum function
∑…→…|… z [[[[[rec]]]]] (+0) ⧗ Number → Number → (Number → Number) → Number
rec (2 =? ++1) case-end case-sum
case-sum 4 (3 + (0 2)) ++2 1 0
case-end 3
:test (∑ (+1) → (+3) | ++‣) ((+9))
# multiplies all values in list
product foldl mul (+1) ⧗ (List Number) → Number
∏‣ product
:test (∏((+1) : ((+2) : {}(+3)))) ((+6))
# equivalent of mathematical product function
∏…→…|… z [[[[[rec]]]]] (+1) ⧗ Number → Number → (Number → Number) → Number
rec (2 =? ++1) case-end case-sum
case-sum 4 (3 ⋅ (0 2)) ++2 1 0
case-end 3
:test (∏ (+1) → (+3) | ++‣) ((+24))
# greatest common divisor
gcd z [[[(1 =? 0) case-eq ((1 >? 0) case-gre case-les)]]] ⧗ Number → Number → Number
case-eq 1
case-gre 2 (1 - 0) 0
case-les 2 1 (0 - 1)
:test ((gcd (+2) (+4)) =? (+2)) (true)
:test ((gcd (+10) (+5)) =? (+5)) (true)
:test ((gcd (+3) (+8)) =? (+1)) (true)
# power function
pow […!!… (iterate (…⋅… 0) (+1))] ⧗ Number → Number → Number
…**… pow
:test (((+2) ** (+3)) =? (+8)) (true)
# power function using ternary exponentiation (TODO: fix, wrong..)
pow* z [[[rec]]] ⧗ Number → Number → Number
rec =?0 case-end case-pow
case-pow =?(lst 0) ³(2 1 /³0) (³(2 1 /³0) ⋅ 1)
³‣ [0 ⋅ 0 ⋅ 0]
case-end (+1)
# prime number sequence
primes nub ((…≠?… (+1)) ∘∘ gcd) (iterate ++‣ (+2)) ⧗ (List Number)
# factorial function
# TODO: faster fac?
fac [∏ (+1) → 0 | i] ⧗ Number → Number
:test ((fac (+3)) =? (+6)) (true)
# fibonacci sequence
# TODO: faster fib?
fibs head <$> (iterate [~0 : (^0 + ~0)] ((+0) : (+1))) ⧗ (List Number)
fib [fibs !! ++0] ⧗ Number
:test (fib (+5)) ((+8))
# integer logarithm
log z [[[[rec]]]] (+1) ⧗ Number → Number → Number
rec [((3 ≤? 1) ⋀? (1 <? 0)) case-end case-rec] (2 ⋅ 1)
case-end (+0)
case-rec ++(4 0 2 1)
:test ((log (+2) (+1)) =? (+0)) (true)
:test ((log (+2) (+2)) =? (+1)) (true)
:test ((log (+2) (+3)) =? (+1)) (true)
:test ((log (+2) (+4)) =? (+2)) (true)
:test ((log (+2) (+32)) =? (+5)) (true)
:test ((log (+2) (+48)) =? (+5)) (true)
# iterated logarithm
# note that log* 1 is defined as 1
log* [z [[rec]] --0] ⧗ Number → Number
rec (0 ≤? (+1)) case-end case-rec
case-end (+1)
case-rec ++(1 (log (+2) 0))
:test ((log* (+1)) =? (+1)) (true)
:test ((log* (+2)) =? (+1)) (true)
:test ((log* (+3)) =? (+2)) (true)
:test ((log* (+4)) =? (+2)) (true)
:test ((log* (+5)) =? (+3)) (true)
:test ((log* (+16)) =? (+3)) (true)
:test ((log* (+17)) =? (+4)) (true)
:test ((log* (+65536)) =? (+4)) (true)
:test ((log* (+65537)) =? (+5)) (true)
# pascal triangle
# TODO: something is wrong in here
pascal iterate [zip-with …+… ({}(+0) ++ 0) (0 ; (+0))] ({}(+1))
# π as a list of decimal digits
# translation of unbounded spigot algorithm by Jeremy Gibbons
# TODO: faster!
# → BBP/Bellard's formula with ternary base?
# TODO: |log|, better primes/mod/div
π g (+1) (+180) (+60) (+2) ⧗ (List Number)
g z [[[[[calc]]]]]
calc b : (4 q r t i)
a ↑⁰(↑⁺0 ⋅ (↑⁰0 + (+2)))
b (3 ⋅ ↑⁰(↑⁻(↑⁻0)) + ((+5) ⋅ 2)) / ((+5) ⋅ 1)
q (+10) ⋅ 3 ⋅ 0 ⋅ --((+2) ⋅ 0)
r (+10) ⋅ a ⋅ (3 ⋅ ((+5) ⋅ 0 - (+2)) + 2 - (b ⋅ 1))
t 1 ⋅ a
i ++0
|
