From 8044eb95639d96512c8891b0c4dca11a4e9e162a Mon Sep 17 00:00:00 2001
From: Marvin Borner <git@marvinborner.de>
Date: Fri, 17 May 2024 13:33:53 +0200
Subject: [PATCH] Minor additions :)

---
 samples/fun/goldbach.bruijn        | 20 ++++++++++++++++++++
 samples/fun/halting_problem.bruijn | 10 ++++++++++
 samples/fun/huge.bruijn            | 16 +++++++++++++++-
 std/Math/Real.bruijn               | 12 +++++++++++-
 4 files changed, 56 insertions(+), 2 deletions(-)
 create mode 100644 samples/fun/goldbach.bruijn
 create mode 100644 samples/fun/halting_problem.bruijn

diff --git a/samples/fun/goldbach.bruijn b/samples/fun/goldbach.bruijn
new file mode 100644
index 0000000..2592a40
--- /dev/null
+++ b/samples/fun/goldbach.bruijn
@@ -0,0 +1,20 @@
+# Tromp's version, will reduce to [0] iff Goldbach conjecture is false
+:import std/Combinator .
+
+zero [[1]]
+
+one [[0]]
+
+sieve y [[[0 one (2 sn1 f)]]]
+	f y [sn2 0]
+		sn2 [[0 (0 4 1)] [[[[0 2 (1 3)]]]]]
+	sn1 [[0 (0 3 1)] [[[[0 2 (1 3)]]]]]
+
+zeroS [[[[0 zero (1 3)]]]]
+
+primes sieve zeroS
+
+check y [[[[[primes 0 (1 (4 0))] testp1]]]]
+	testp1 [0 0 2 [0 4] 0]
+
+main primes (check [[[[0]]]])
diff --git a/samples/fun/halting_problem.bruijn b/samples/fun/halting_problem.bruijn
new file mode 100644
index 0000000..dd7e6d6
--- /dev/null
+++ b/samples/fun/halting_problem.bruijn
@@ -0,0 +1,10 @@
+:import std/Logic .
+
+# hypothetical halting decider (shall not loop)
+# assuming (Program Arg) reduces to boolean
+halting [[halts (1 0)]] ⧗ Program → Arg → Boolean
+	halts [0 true false]
+
+# basically y combinator
+# paradox!
+e halting [¬(halting 0 0)] [¬(halting 0 0)]
diff --git a/samples/fun/huge.bruijn b/samples/fun/huge.bruijn
index 2d963ad..2f36dc1 100644
--- a/samples/fun/huge.bruijn
+++ b/samples/fun/huge.bruijn
@@ -1,4 +1,18 @@
 # "bruijn huge.bruijn"
+# some of the fastest growing functions per blc length
+
 # 55 bits inflating to 65536 bits, John Tromp
+huge-55 [[0 0 0 0 [[0 [[0]] 1]]] (+2u)
+
+# 64 bits inflating to ??? bits, John Tromp
+huge-64 [0 0 h 0 0 0] (+2u)
+	h [[[0 2 1 0]]]
+
+# 79 bits inflating to ??? bits, John Tromp and Bertram Felgenhauer
+huge-79 [0 0 e 0] (+2u)
+	e [0 g [[0]] d0 0]
+		g [[1 (d 0) (0 [0])]]
+			d [[[2 [2 0 1]]]]
+		d0 [[1 0 0]]
 
-main [[0 0 0 0 [[0 [[0]] 1]]] [[1 (1 0)]]]
+main huge-64
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