std/Math/Real.bruijn


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# some ideas by u/DaVinci103
# MIT License, Copyright (c) 2024 Marvin Borner

:import std/Logic .
:import std/Combinator .
:import std/Math/Rational .
:import std/Number N

# converts a balanced ternary number to a real number
number→real [[number→rational 1]] ⧗ Number → Real

:test (number→real (+5)) ((+5.0r))

approx-eq? [[[eq? (1 2) (0 2)]]] ⧗ Number → Real → Real → Boolean

# TODO: bigger value (higher performance first!)
…≈?… approx-eq? (+1000)

# TODO: this value could turn the whole equation to garbage (e.g. in div x ε)
ε (+0.000000000000000000000001)

# extends φ combinator by canceling further reductions when approximator hits 0
φ-lim [[[[[N.=?0 ε (4 (3 0) (2 0))] N.--0]]]]

# extends b combinator by canceling further reductions when approximator hits 0
b-lim [[[N.=?0 ε (2 (1 N.--0))]]]

# adds two real numbers
add φ-lim add ⧗ Real → Real → Real

…+… add

# subtracts two real numbers
sub φ-lim sub ⧗ Real → Real → Real

…-… sub

# multiplies two real numbers
mul φ-lim mul ⧗ Real → Real → Real

…⋅… mul

# divides two real numbers
div φ-lim div ⧗ Real → Real → Real

…/… div

# negates a real number
negate b-lim negate ⧗ Real → Real

-‣ negate

# inverts a real number
invert b-lim invert ⧗ Real → Real

~‣ invert

# finds smallest equivalent representation of a real number
compress b-lim compress ⧗ Real → Real

%‣ compress

# ---

:import std/List .

# for debugging
…#… φ-lim cons

# real^number
pow-n […!!… (iterate (mul 0) (+1.0r))] ⧗ Real → Number → Real

exp [y [[[[rec]]]] (+1) (+1.0r) (+1.0r)]
	rec (1 / 0) + (3 N.++2 (1 ⋅ 4) (0 ⋅ (number→real 2)))

ln [y [[[rec]]] (+1) 0]
	rec (N.=²?1 -‣ [0] (0 / (number→real 1))) + (2 N.++1 (3 ⋅ 0))

# power function
pow [[exp (0 ⋅ (ln 1))]] ⧗ Real → Real → Real

…**… pow

# :test (((+2.0r) ** (+3.0r)) ≈? (+8.0r)) (true)