commit 0e372df756b492ef43a3d2061ed1cb88bc086f1f
Author: hal8174 <henning.lindemann@pm.me>
Date:   Sat Sep 21 22:26:15 2024 +0200

    Initial commit.

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..b9762b6
--- /dev/null
+++ b/Cargo.lock
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diff --git a/Cargo.toml b/Cargo.toml
new file mode 100644
index 0000000..04e7b13
--- /dev/null
+++ b/Cargo.toml
@@ -0,0 +1,11 @@
+[package]
+name = "bitexperimentation"
+version = "0.1.0"
+edition = "2021"
+
+[dependencies]
+
+
+[dev-dependencies]
+quickcheck = "1"
+quickcheck_macros = "1"
diff --git a/src/main.rs b/src/main.rs
new file mode 100644
index 0000000..5d9aff1
--- /dev/null
+++ b/src/main.rs
@@ -0,0 +1,156 @@
+#[allow(non_snake_case)]
+fn L(k: u8) -> u64 {
+    let mut s = 0;
+    for i in 0..64u8.div_ceil(k) {
+        s |= 1 << (i * k);
+    }
+    s
+}
+
+#[allow(non_snake_case)]
+fn H(k: u8) -> u64 {
+    L(k) << (k - 1)
+}
+
+fn sideways_addition(x: u64) -> u64 {
+    let s = x - ((x & 0xAAAAAAAAAAAAAAAA) >> 1);
+    // 0xA = 0b1010
+    let s = (s & 0x3333333333333333) + ((s >> 2) & 0x3333333333333333);
+    // 0x3 = 0b0011
+    let s = (s + (s >> 4)) & 0x0F0F0F0F0F0F0F0F;
+    u64::wrapping_mul(s, L(8)) >> 56
+}
+
+fn less_equal_k_signed(x: u64, y: u64, k: u8) -> u64 {
+    let s = (y | H(k)) - (x & !H(k));
+    let s = s ^ x ^ y;
+    let s = s | (x & !y);
+    let s = s & !(!x & y);
+    s & H(k)
+}
+
+fn less_equal_k_unsigned(x: u64, y: u64, k: u8) -> u64 {
+    let s = (y | H(k)) - (x & !H(k));
+    let s = s | x ^ y;
+    let s = s ^ (x & !y);
+    s & H(k)
+}
+
+fn grater_than_0_k_unsigned(x: u64, k: u8) -> u64 {
+    (((x | H(k)) - L(k)) | x) & H(k)
+}
+
+fn select64(x: u64, r: u64) -> u64 {
+    // Same as in sideways addition
+    let s = x - ((x & 0xAAAAAAAAAAAAAAAA) >> 1);
+    // 0xA = 0b1010
+    let s = (s & 0x3333333333333333) + ((s >> 2) & 0x3333333333333333);
+    // 0x3 = 0b0011
+    let s = ((s + (s >> 4)) & 0x0F0F0F0F0F0F0F0F).wrapping_mul(L(8));
+
+    // Select byte
+    // b: byte index << 3
+    let b =
+        (less_equal_k_signed(s, r.wrapping_mul(L(8)), 8) >> 7).wrapping_mul(L(8)) >> 53 & (!0x7);
+    if b == 64 {
+        return 72;
+    }
+
+    // extract selected byte
+    let l = r - (((s << 8) >> b) & 0xFF);
+
+    // select index in byte
+    let s = (grater_than_0_k_unsigned((x >> b & 0xFF).wrapping_mul(L(8)) & 0x8040201008040201, 8)
+        >> 7)
+        .wrapping_mul(L(8));
+
+    b + ((less_equal_k_signed(s, l.wrapping_mul(L(8)), 8) >> 7).wrapping_mul(L(8)) >> 56)
+}
+
+fn trivial_select(data: u64, count: u8) -> u8 {
+    let mut l = 0;
+    let mut r = 63;
+
+    while l < r {
+        let m = (l + r) / 2;
+
+        let shift = 64 - m - 1;
+        let shifted = data << shift;
+
+        let local_count = shifted.count_ones();
+
+        // dbg!(l, r, m, shift, local_count, r);
+
+        if local_count < count as u32 {
+            l = m + 1;
+        } else {
+            r = m;
+        }
+    }
+    l as u8
+}
+
+fn main() {
+    dbg!(select64(3, 1));
+    dbg!(trivial_select(3, 3));
+}
+
+#[cfg(test)]
+mod test {
+    use quickcheck_macros::quickcheck;
+
+    use crate::*;
+
+    #[quickcheck]
+    fn qc_test_sideways_addition(x: u64) -> bool {
+        x.count_ones() as u64 == sideways_addition(x)
+    }
+
+    #[quickcheck]
+    fn qc_less_equal_8_signed(x: u64, y: u64) -> bool {
+        let s = less_equal_k_signed(x, y, 8).to_be_bytes();
+
+        s.iter()
+            .zip(x.to_be_bytes().iter().zip(y.to_be_bytes().iter()))
+            .all(|(s, (&x, &y))| match s {
+                0x00 => (x as i8) > (y as i8),
+                0x80 => (x as i8) <= (y as i8),
+                _ => false,
+            })
+    }
+
+    #[quickcheck]
+    fn qc_less_equal_k_unsigned(x: u64, y: u64) -> bool {
+        let s = less_equal_k_unsigned(x, y, 8).to_be_bytes();
+
+        s.iter()
+            .zip(x.to_be_bytes().iter().zip(y.to_be_bytes().iter()))
+            .all(|(s, (&x, &y))| match s {
+                0x00 => x > y,
+                0x80 => x <= y,
+                _ => false,
+            })
+    }
+
+    #[quickcheck]
+    fn qc_grater_than_0_k_unsigned(x: u64) -> bool {
+        let s = grater_than_0_k_unsigned(x, 8).to_be_bytes();
+        s.iter().zip(x.to_be_bytes().iter()).all(|(a, b)| match a {
+            0x00 => b == &0,
+            0x80 => b > &0,
+            _ => false,
+        })
+    }
+
+    #[quickcheck]
+    fn qc_select64(x: u64, r: u8) -> bool {
+        let r = r.clamp(1, 64);
+        let s = select64(x, r as u64);
+
+        if x.count_ones() <= r as u32 {
+            s == 72
+        } else {
+            trivial_select(x, r + 1) as u64 == s
+        }
+    }
+}