mirror of
https://github.com/pezkuwichain/pezkuwi-subxt.git
synced 2026-04-26 12:17:58 +00:00
Benjamin Kampmann
114 lines
3.8 KiB
Rust
114 lines
3.8 KiB
Rust
// This file is part of Substrate.
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// Copyright (C) 2019-2020 Parity Technologies (UK) Ltd.
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// SPDX-License-Identifier: Apache-2.0
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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//! Some helper functions to work with 128bit numbers. Note that the functionality provided here is
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//! only sensible to use with 128bit numbers because for smaller sizes, you can always rely on
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//! assumptions of a bigger type (u128) being available, or simply create a per-thing and use the
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//! multiplication implementation provided there.
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use crate::biguint;
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use num_traits::Zero;
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use sp_std::{cmp::{min, max}, convert::TryInto, mem};
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/// Helper gcd function used in Rational128 implementation.
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pub fn gcd(a: u128, b: u128) -> u128 {
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match ((a, b), (a & 1, b & 1)) {
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((x, y), _) if x == y => y,
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((0, x), _) | ((x, 0), _) => x,
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((x, y), (0, 1)) | ((y, x), (1, 0)) => gcd(x >> 1, y),
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((x, y), (0, 0)) => gcd(x >> 1, y >> 1) << 1,
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((x, y), (1, 1)) => {
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let (x, y) = (min(x, y), max(x, y));
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gcd((y - x) >> 1, x)
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},
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_ => unreachable!(),
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}
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}
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/// split a u128 into two u64 limbs
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pub fn split(a: u128) -> (u64, u64) {
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let al = a as u64;
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let ah = (a >> 64) as u64;
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(ah, al)
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}
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/// Convert a u128 to a u32 based biguint.
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pub fn to_big_uint(x: u128) -> biguint::BigUint {
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let (xh, xl) = split(x);
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let (xhh, xhl) = biguint::split(xh);
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let (xlh, xll) = biguint::split(xl);
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let mut n = biguint::BigUint::from_limbs(&[xhh, xhl, xlh, xll]);
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n.lstrip();
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n
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}
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/// Safely and accurately compute `a * b / c`. The approach is:
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/// - Simply try `a * b / c`.
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/// - Else, convert them both into big numbers and re-try. `Err` is returned if the result
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/// cannot be safely casted back to u128.
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///
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/// Invariant: c must be greater than or equal to 1.
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pub fn multiply_by_rational(mut a: u128, mut b: u128, mut c: u128) -> Result<u128, &'static str> {
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if a.is_zero() || b.is_zero() { return Ok(Zero::zero()); }
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c = c.max(1);
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// a and b are interchangeable by definition in this function. It always helps to assume the
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// bigger of which is being multiplied by a `0 < b/c < 1`. Hence, a should be the bigger and
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// b the smaller one.
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if b > a {
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mem::swap(&mut a, &mut b);
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}
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// Attempt to perform the division first
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if a % c == 0 {
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a /= c;
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c = 1;
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} else if b % c == 0 {
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b /= c;
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c = 1;
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}
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if let Some(x) = a.checked_mul(b) {
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// This is the safest way to go. Try it.
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Ok(x / c)
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} else {
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let a_num = to_big_uint(a);
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let b_num = to_big_uint(b);
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let c_num = to_big_uint(c);
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let mut ab = a_num * b_num;
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ab.lstrip();
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let mut q = if c_num.len() == 1 {
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// PROOF: if `c_num.len() == 1` then `c` fits in one limb.
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ab.div_unit(c as biguint::Single)
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} else {
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// PROOF: both `ab` and `c` cannot have leading zero limbs; if length of `c` is 1,
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// the previous branch would handle. Also, if ab for sure has a bigger size than
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// c, because `a.checked_mul(b)` has failed, hence ab must be at least one limb
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// bigger than c. In this case, returning zero is defensive-only and div should
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// always return Some.
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let (mut q, r) = ab.div(&c_num, true).unwrap_or((Zero::zero(), Zero::zero()));
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let r: u128 = r.try_into()
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.expect("reminder of div by c is always less than c; qed");
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if r > (c / 2) { q = q.add(&to_big_uint(1)); }
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q
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};
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q.lstrip();
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q.try_into().map_err(|_| "result cannot fit in u128")
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}
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}
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