From ad4c09192e6144e3e914748f9ce4edf371cf75b8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Juan=20Manuel=20Tom=C3=A1s?= <jtomas1815@gmail.com>
Date: Thu, 7 Jan 2021 11:57:02 -0300
Subject: Initial commit

Starting off with a function able to turn recursive linear
interpolations into their corresponding polynomial.
---
 .gitignore  |  1 +
 Cargo.lock  |  5 +++++
 Cargo.toml  |  9 +++++++++
 src/lib.rs  | 53 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 src/main.rs |  5 +++++
 5 files changed, 73 insertions(+)
 create mode 100644 .gitignore
 create mode 100644 Cargo.lock
 create mode 100644 Cargo.toml
 create mode 100644 src/lib.rs
 create mode 100644 src/main.rs

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..ea8c4bf
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1 @@
+/target
diff --git a/Cargo.lock b/Cargo.lock
new file mode 100644
index 0000000..b1c5475
--- /dev/null
+++ b/Cargo.lock
@@ -0,0 +1,5 @@
+# This file is automatically @generated by Cargo.
+# It is not intended for manual editing.
+[[package]]
+name = "poly"
+version = "0.1.0"
diff --git a/Cargo.toml b/Cargo.toml
new file mode 100644
index 0000000..ab64b5d
--- /dev/null
+++ b/Cargo.toml
@@ -0,0 +1,9 @@
+[package]
+name = "poly"
+version = "0.1.0"
+authors = ["Juan Manuel Tomás <jtomas1815@gmail.com>"]
+edition = "2018"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]
diff --git a/src/lib.rs b/src/lib.rs
new file mode 100644
index 0000000..31f230e
--- /dev/null
+++ b/src/lib.rs
@@ -0,0 +1,53 @@
+pub type Number = f32;
+
+pub type Poly = Vec<Number>;
+
+#[derive(Debug)]
+pub enum Lerp {
+    Node(Box<Lerp>, Box<Lerp>),
+    Leaf(Number, Number)
+}
+
+impl Lerp {
+    pub fn new(v: Vec<Number>) -> Box<Lerp> {
+        Lerp::new_s(&v[..])
+    }
+
+    fn new_s(v: &[Number]) -> Box<Lerp> {
+        match v.len() {
+            0 => Box::new(Lerp::Leaf(0.0, 0.0)),
+            1 => Box::new(Lerp::Leaf(v[0], v[0])),
+            2 => Box::new(Lerp::Leaf(v[0], v[1])),
+            _ => Box::new(Lerp::Node(Lerp::new_s(&v[0..v.len() - 1]), Lerp::new_s(&v[1..v.len()])))
+        }
+    }
+}
+
+pub fn lp(l: Box<Lerp>) -> Poly {
+    match *l {
+        Lerp::Leaf(a, b) => vec![a, b - a],
+        Lerp::Node(a, b) => {
+            let a = lp(a);
+            let b = lp(b);
+            let c = poly_sub(&b, &a);
+            skewed_sum(a, c)
+        }
+    }
+}
+
+fn poly_sub(a: &Poly, b: &Poly) -> Poly {
+    let mut r = a.clone();
+    for i in 0..r.len() {
+        r[i] -= b[i];
+    }
+    r
+}
+
+fn skewed_sum(a: Poly, b: Poly) -> Poly {
+    let mut r = a.clone();
+    for i in 0..r.len() - 1 {
+        r[i + 1] += b[i];
+    }
+    r.push(b[b.len() - 1]);
+    r
+}
diff --git a/src/main.rs b/src/main.rs
new file mode 100644
index 0000000..1e4f704
--- /dev/null
+++ b/src/main.rs
@@ -0,0 +1,5 @@
+fn main() {
+    let a = poly::Lerp::new(vec![1.0, 5.0, 8.0, 3.0, 10.0]);
+    println!("{:?}", a);
+    println!("{:?}", poly::lp(a));
+}
-- 
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