Module sp_arithmetic::per_things

Types that implement PerThing can be used as a floating-point alternative for numbers that operate within the realm of [0, 1]. The primary types may you encounter in Substrate would be the following:

• Percent - parts of one hundred.
• Permill - parts of a million.
• Perbill - parts of a billion.

In use, you may see them being used as follows:

Perbill, parts of a billion

#[test]
fn perbill_example() {
	let p = Perbill::from_percent(80);
	// 800000000 bil, or a representative of 0.800000000.
	// Precision is in the billions place.
	assert_eq!(p.deconstruct(), 800000000);
}

Percent, parts of a hundred

#[test]
fn percent_example() {
	let percent = Percent::from_rational(190u32, 400u32);
	assert_eq!(percent.deconstruct(), 47);
}

Note that Percent is represented as a rounded down, fixed point number (see the example above). Unlike primitive types, types that implement PerThing will also not overflow, and are therefore safe to use. They adopt the same behavior that a saturated calculation would provide, meaning that if one is to go over “100%”, it wouldn’t overflow, but simply stop at the upper or lower bound.

For use cases which require precision beyond the range of [0, 1], there are fixed-point types which can be used.

Each of these can be used to construct and represent ratios within our runtime. You will find types like Perbill being used often in pallet development. pallet_referenda is a good example of a pallet which makes good use of fixed point arithmetic, as it relies on representing various curves and thresholds relating to governance.

Fixed Point Arithmetic with PerThing

As stated, one can also perform mathematics using these types directly. For example, finding the percentage of a particular item:

#[test]
fn percent_mult() {
	let percent = Percent::from_rational(5u32, 100u32); // aka, 5%
	let five_percent_of_100 = percent * 100u32; // 5% of 100 is 5.
	assert_eq!(five_percent_of_100, 5)
}

Structs

• PerU16
  A fixed point representation of a number in the range [0, 1].
• Perbill
  A fixed point representation of a number in the range [0, 1].
• Percent
  A fixed point representation of a number in the range [0, 1].
• Permill
  A fixed point representation of a number in the range [0, 1].
• Perquintill
  A fixed point representation of a number in the range [0, 1].

Enums

• Rounding
  The rounding method to use for unsigned quantities.
• SignedRounding
  The rounding method to use.

Traits

• MultiplyArg
• PerThing
  Something that implements a fixed point ration with an arbitrary granularity X, as parts per X.
• RationalArg
• ReciprocalArg

Type Aliases

• InnerOf
  Get the inner type of a PerThing.
• UpperOf
  Get the upper type of a PerThing.