sp-arithmetic 2.0.0-alpha.7

Minimal fixed point arithmetic primitives and types for runtime.
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166

// Copyright 2017-2020 Parity Technologies (UK) Ltd.
// This file is part of Substrate.

// Substrate is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// Substrate is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with Substrate.  If not, see <http://www.gnu.org/licenses/>.

//! Primitive traits for the runtime arithmetic.

use sp_std::{self, convert::{TryFrom, TryInto}};
use codec::HasCompact;
pub use integer_sqrt::IntegerSquareRoot;
pub use num_traits::{
	Zero, One, Bounded, CheckedAdd, CheckedSub, CheckedMul, CheckedDiv,
	CheckedShl, CheckedShr, checked_pow
};
use sp_std::ops::{
	Add, Sub, Mul, Div, Rem, AddAssign, SubAssign, MulAssign, DivAssign,
	RemAssign, Shl, Shr
};

/// A meta trait for arithmetic type operations, regardless of any limitation on size.
pub trait BaseArithmetic:
	From<u8> +
	Zero + One + IntegerSquareRoot +
	Add<Self, Output = Self> + AddAssign<Self> +
	Sub<Self, Output = Self> + SubAssign<Self> +
	Mul<Self, Output = Self> + MulAssign<Self> +
	Div<Self, Output = Self> + DivAssign<Self> +
	Rem<Self, Output = Self> + RemAssign<Self> +
	Shl<u32, Output = Self> + Shr<u32, Output = Self> +
	CheckedShl + CheckedShr + CheckedAdd + CheckedSub + CheckedMul + CheckedDiv + Saturating +
	PartialOrd<Self> + Ord + Bounded + HasCompact + Sized +
	TryFrom<u8> + TryInto<u8> + TryFrom<u16> + TryInto<u16> + TryFrom<u32> + TryInto<u32> +
	TryFrom<u64> + TryInto<u64> + TryFrom<u128> + TryInto<u128> + TryFrom<usize> + TryInto<usize> +
	UniqueSaturatedFrom<u8> + UniqueSaturatedInto<u8> +
	UniqueSaturatedFrom<u16> + UniqueSaturatedInto<u16> +
	UniqueSaturatedFrom<u32> + UniqueSaturatedInto<u32> +
	UniqueSaturatedFrom<u64> + UniqueSaturatedInto<u64> +
	UniqueSaturatedFrom<u128> + UniqueSaturatedInto<u128>
{}

impl<T:
	From<u8> +
	Zero + One + IntegerSquareRoot +
	Add<Self, Output = Self> + AddAssign<Self> +
	Sub<Self, Output = Self> + SubAssign<Self> +
	Mul<Self, Output = Self> + MulAssign<Self> +
	Div<Self, Output = Self> + DivAssign<Self> +
	Rem<Self, Output = Self> + RemAssign<Self> +
	Shl<u32, Output = Self> + Shr<u32, Output = Self> +
	CheckedShl + CheckedShr + CheckedAdd + CheckedSub + CheckedMul + CheckedDiv + Saturating +
	PartialOrd<Self> + Ord + Bounded + HasCompact + Sized +
	TryFrom<u8> + TryInto<u8> + TryFrom<u16> + TryInto<u16> + TryFrom<u32> + TryInto<u32> +
	TryFrom<u64> + TryInto<u64> + TryFrom<u128> + TryInto<u128> + TryFrom<usize> + TryInto<usize> +
	UniqueSaturatedFrom<u8> + UniqueSaturatedInto<u8> +
	UniqueSaturatedFrom<u16> + UniqueSaturatedInto<u16> +
	UniqueSaturatedFrom<u32> + UniqueSaturatedInto<u32> +
	UniqueSaturatedFrom<u64> + UniqueSaturatedInto<u64> +
	UniqueSaturatedFrom<u128> + UniqueSaturatedInto<u128>
> BaseArithmetic for T {}

/// A meta trait for arithmetic.
///
/// Arithmetic types do all the usual stuff you'd expect numbers to do. They are guaranteed to
/// be able to represent at least `u32` values without loss, hence the trait implies `From<u32>`
/// and smaller integers. All other conversions are fallible.
pub trait AtLeast32Bit: BaseArithmetic + From<u16> + From<u32> {}

impl<T: BaseArithmetic + From<u16> + From<u32>> AtLeast32Bit for T {}

/// Just like `From` except that if the source value is too big to fit into the destination type
/// then it'll saturate the destination.
pub trait UniqueSaturatedFrom<T: Sized>: Sized {
	/// Convert from a value of `T` into an equivalent instance of `Self`.
	fn unique_saturated_from(t: T) -> Self;
}

/// Just like `Into` except that if the source value is too big to fit into the destination type
/// then it'll saturate the destination.
pub trait UniqueSaturatedInto<T: Sized>: Sized {
	/// Consume self to return an equivalent value of `T`.
	fn unique_saturated_into(self) -> T;
}

impl<T: Sized, S: TryFrom<T> + Bounded + Sized> UniqueSaturatedFrom<T> for S {
	fn unique_saturated_from(t: T) -> Self {
		S::try_from(t).unwrap_or_else(|_| Bounded::max_value())
	}
}

impl<T: Bounded + Sized, S: TryInto<T> + Sized> UniqueSaturatedInto<T> for S {
	fn unique_saturated_into(self) -> T {
		self.try_into().unwrap_or_else(|_| Bounded::max_value())
	}
}

/// Saturating arithmetic operations, returning maximum or minimum values instead of overflowing.
pub trait Saturating {
	/// Saturating addition. Compute `self + rhs`, saturating at the numeric bounds instead of
	/// overflowing.
	fn saturating_add(self, rhs: Self) -> Self;

	/// Saturating subtraction. Compute `self - rhs`, saturating at the numeric bounds instead of
	/// overflowing.
	fn saturating_sub(self, rhs: Self) -> Self;

	/// Saturating multiply. Compute `self * rhs`, saturating at the numeric bounds instead of
	/// overflowing.
	fn saturating_mul(self, rhs: Self) -> Self;

	/// Saturating exponentiation. Compute `self.pow(exp)`, saturating at the numeric bounds
	/// instead of overflowing.
	fn saturating_pow(self, exp: usize) -> Self;
}

impl<T: Clone + One + CheckedMul + Bounded + num_traits::Saturating> Saturating for T {
	fn saturating_add(self, o: Self) -> Self {
		<Self as num_traits::Saturating>::saturating_add(self, o)
	}

	fn saturating_sub(self, o: Self) -> Self {
		<Self as num_traits::Saturating>::saturating_sub(self, o)
	}

	fn saturating_mul(self, o: Self) -> Self {
		self.checked_mul(&o).unwrap_or_else(Bounded::max_value)
	}

	fn saturating_pow(self, exp: usize) -> Self {
		checked_pow(self, exp).unwrap_or_else(Bounded::max_value)
	}
}

/// Convenience type to work around the highly unergonomic syntax needed
/// to invoke the functions of overloaded generic traits, in this case
/// `SaturatedFrom` and `SaturatedInto`.
pub trait SaturatedConversion {
	/// Convert from a value of `T` into an equivalent instance of `Self`.
	///
	/// This just uses `UniqueSaturatedFrom` internally but with this
	/// variant you can provide the destination type using turbofish syntax
	/// in case Rust happens not to assume the correct type.
	fn saturated_from<T>(t: T) -> Self where Self: UniqueSaturatedFrom<T> {
		<Self as UniqueSaturatedFrom<T>>::unique_saturated_from(t)
	}

	/// Consume self to return an equivalent value of `T`.
	///
	/// This just uses `UniqueSaturatedInto` internally but with this
	/// variant you can provide the destination type using turbofish syntax
	/// in case Rust happens not to assume the correct type.
	fn saturated_into<T>(self) -> T where Self: UniqueSaturatedInto<T> {
		<Self as UniqueSaturatedInto<T>>::unique_saturated_into(self)
	}
}
impl<T: Sized> SaturatedConversion for T {}