Rename Palette to FRAME (#4182)

* palette -> frame

* PALETTE, Palette -> FRAME

* Move folder pallete -> frame

* Update docs/Structure.adoc

Co-Authored-By: Benjamin Kampmann <ben.kampmann@googlemail.com>

* Update docs/README.adoc

Co-Authored-By: Benjamin Kampmann <ben.kampmann@googlemail.com>

* Update README.adoc

substrate/frame/staking/reward-curve/src/log.rs

@@ -0,0 +1,70 @@
+use std::convert::TryInto;
+
+/// Return Per-million value.
+pub fn log2(p: u32, q: u32) -> u32 {
+	assert!(p >= q);
+	assert!(p <= u32::max_value()/2);
+
+	// This restriction should not be mandatory. But function is only tested and used for this.
+	assert!(p <= 1_000_000);
+	assert!(q <= 1_000_000);
+
+	if p == q {
+		return 0
+	}
+
+	let mut n = 0u32;
+	while !(p >= 2u32.pow(n)*q) || !(p < 2u32.pow(n+1)*q) {
+		n += 1;
+	}
+	assert!(p < 2u32.pow(n+1) * q);
+
+	let y_num: u32 = (p - 2u32.pow(n) * q).try_into().unwrap();
+	let y_den: u32 = (p + 2u32.pow(n) * q).try_into().unwrap();
+
+	let _2_div_ln_2 = 2_885_390u32;
+
+	let taylor_term = |k: u32| -> u32 {
+		if k == 0 {
+			(_2_div_ln_2 as u128 * (y_num as u128).pow(1) / (y_den as u128).pow(1))
+				.try_into().unwrap()
+		} else {
+			let mut res = _2_div_ln_2 as u128 * (y_num as u128).pow(3) / (y_den as u128).pow(3);
+			for _ in 1..k {
+				res = res * (y_num as u128).pow(2) / (y_den as u128).pow(2);
+			}
+			res /= 2 * k as u128 + 1;
+
+			res.try_into().unwrap()
+		}
+	};
+
+	let mut res = n * 1_000_000u32;
+	let mut k = 0;
+	loop {
+		let term = taylor_term(k);
+		if term == 0 {
+			break
+		}
+
+		res += term;
+		k += 1;
+	}
+
+	res
+}
+
+#[test]
+fn test_log() {
+	let div = 1_000;
+	for p in 0..=div {
+		for q in 1..=p {
+			let p: u32 = (1_000_000 as u64 * p as u64 / div as u64).try_into().unwrap();
+			let q: u32 = (1_000_000 as u64 * q as u64 / div as u64).try_into().unwrap();
+
+			let res = - (log2(p, q) as i64);
+			let expected = ((q as f64 / p as f64).log(2.0) * 1_000_000 as f64).round() as i64;
+			assert!((res - expected).abs() <= 6);
+		}
+	}
+}