Implement FixedPoint trait. (#5877)

* Implement Fixed trait.

* Fix tests

* Fix tests

* Fix tests 2

* Address review comment regarding from_i129.

* Remove precision by using log10() as suggested in review.

* Add small comments.

* Use checked versions + panic for ops::*.

* Remove repeated test.

* Uncomment test.

* Remove casts.

* Add more comments.

* Add tests.

* Panic on saturating_div_int

* More tests.

* More docs.

* Saturating renames.

* Fix to_bound doc.

* Move some impl to trait.

* Add range

* Add macro pre.

* More round() tests.

* Delete confusion.

* More impl to trait

* Add doc for fixedpoint op.

* Remove trailing spaces.

* Suggested docs changes.

* More tests and comments for roundings.

* Some quickcheck tests.

* Add missing panic, more test/comments.

* Nits.

* Rename.

* Remove primitives-types import.

* Apply review suggestions

* Fix long lines and add some fuzz.

* fix long line

* Update fuzzer

* Bump impl

* fix warnings

Co-authored-by: Gavin Wood <gavin@parity.io>
Co-authored-by: Shawn Tabrizi <shawntabrizi@gmail.com>

substrate/primitives/arithmetic/fuzzer/src/fixed.rs

@@ -0,0 +1,82 @@
+// This file is part of Substrate.
+
+// Copyright (C) 2020 Parity Technologies (UK) Ltd.
+// SPDX-License-Identifier: Apache-2.0
+
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// 	http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+//! # Running
+//! Running this fuzzer can be done with `cargo hfuzz run fixed`. `honggfuzz` CLI options can
+//! be used by setting `HFUZZ_RUN_ARGS`, such as `-n 4` to use 4 threads.
+//!
+//! # Debugging a panic
+//! Once a panic is found, it can be debugged with
+//! `cargo hfuzz run-debug fixed hfuzz_workspace/fixed/*.fuzz`.
+//!
+//! # More information
+//! More information about `honggfuzz` can be found
+//! [here](https://docs.rs/honggfuzz/).
+
+use honggfuzz::fuzz;
+use sp_arithmetic::{FixedPointNumber, Fixed64, traits::Saturating};
+
+fn main() {
+	loop {
+		fuzz!(|data: (i32, i32)| {
+			let x: i128 = data.0.into();
+			let y: i128 = data.1.into();
+
+			// Check `from_rational` and division are consistent.
+			if y != 0 {
+				let f1 = Fixed64::saturating_from_integer(x) / Fixed64::saturating_from_integer(y);
+				let f2 = Fixed64::saturating_from_rational(x, y);
+				assert_eq!(f1.into_inner(), f2.into_inner());
+			}
+
+			// Check `saturating_mul`.
+			let a = Fixed64::saturating_from_rational(2, 5);
+			let b = a.saturating_mul(Fixed64::saturating_from_integer(x));
+			let n = b.into_inner() as i128;
+			let m = 2i128 * x * Fixed64::accuracy() as i128 / 5i128;
+			assert_eq!(n, m);
+
+			// Check `saturating_mul` and division are inverse.
+			if x != 0 {
+				assert_eq!(a, b / Fixed64::saturating_from_integer(x));
+			}
+
+			// Check `reciprocal`.
+			let r = a.reciprocal().unwrap().reciprocal().unwrap();
+			assert_eq!(a, r);
+
+			// Check addition.
+			let a = Fixed64::saturating_from_integer(x);
+			let b = Fixed64::saturating_from_integer(y);
+			let c = Fixed64::saturating_from_integer(x.saturating_add(y));
+			assert_eq!(a.saturating_add(b), c);
+
+			// Check substraction.
+			let a = Fixed64::saturating_from_integer(x);
+			let b = Fixed64::saturating_from_integer(y);
+			let c = Fixed64::saturating_from_integer(x.saturating_sub(y));
+			assert_eq!(a.saturating_sub(b), c);
+
+			// Check `saturating_mul_acc_int`.
+			let a = Fixed64::saturating_from_rational(2, 5);
+			let b = a.saturating_mul_acc_int(x);
+			let xx = Fixed64::saturating_from_integer(x);
+			let d = a.saturating_mul(xx).saturating_add(xx).into_inner() as i128 / Fixed64::accuracy() as i128;
+			assert_eq!(b, d);
+		});
+	}
+}