Crate primitive_fixed_point_decimal 

Primitive fixed-point decimal types.

Fixed-point: The scale is bound to type. All instances under one type have the same fraction precision and won’t change in their whole lifetime.

Decimal: It represents decimal fractions accurately by scaling integers in base-10. So there is no round-off error like 0.1 + 0.2 != 0.3.

Therefore, it is especially suitable for financial use cases, along with many others.

See the Comparison section for details.

Features

Important:

• The + and - operations only perform between same types in same scale. There is no implicitly type or scale conversion. This makes sense, for we do not want to add Balance type by Price type.

• The * and / operations accept operand with different types and scales, and allow the result’s scale specified. Certainly we need to multiply between Balance type and Price type.

• Supports 2 ways to specify the scale: const and out-of-band. See the Specify Scale section for details.

• Supports all primitive integers as the underlying types: short, long, signed and unsigned.

• Compact memory and high performance. See the benchmark for details.

Less important, yet might also be what you need:

• Supports scale larger than the significant digits of the underlying integer type. For example ConstScaleFpdec<i8, 4> represents numbers in range [-0.0128, 0.0127].

• Supports negative scale. For example ConstScaleFpdec<i8, -2> represents numbers in range [-12800, 12700] with step 100.

• Supports serde traits integration (Serialize/Deserialize) by optional serde feature flag.

• no-std and no-alloc.

Usage

Here we take ConstScaleFpdec as example. The other type OobScaleFpdec is similar. See the Specify Scale section for details.

There are several ways to construct the decimal:

use primitive_fixed_point_decimal::{ConstScaleFpdec, fpdec};

// We choose `i64` as the underlying integer, and keep `4` precision.
type Balance = ConstScaleFpdec<i64, 4>;

// From float or integer number.
let _b1 = Balance::try_from(12.34).unwrap();
let _b2 = Balance::try_from(1234).unwrap();

// The macro `fpdec` wraps above 2 TryFrom methods. It panics if fail in convert.
let _b1: Balance = fpdec!(12.34);
let _b2: Balance = fpdec!(1234);

// From string.
use std::str::FromStr;
let _b = Balance::from_str("12.34").unwrap();

// From mantissa, which is the underlying integer.
// This is low-level, but also the only `const` construction method.
const TWENTY: Balance = Balance::from_mantissa(20 * 10000);

Addition and substraction operations only perform between same types in same scale. There is no implicitly type or scale conversion. This make them super fast, roughly equivalent to one single CPU instruction.

use primitive_fixed_point_decimal::{ConstScaleFpdec, fpdec};
type Balance = ConstScaleFpdec<i64, 4>;

let b1: Balance = fpdec!(12.34);
let b2: Balance = fpdec!(8000);

assert_eq!(b1 + b2, fpdec!(8012.34));

// If you want to check the overflow, use `checked_add()`:
assert_eq!(b1.checked_add(b2), Some(fpdec!(8012.34)));
assert_eq!(b1.checked_add(Balance::MAX), None);

Multiplication and division operations accept operand with different types and scales, and allow the result’s scale specified.

use primitive_fixed_point_decimal::{ConstScaleFpdec, fpdec, Rounding};
type Balance = ConstScaleFpdec<i64, 4>;

// new type with different integer type and precision
type FeeRate = ConstScaleFpdec<u16, 6>;

let b: Balance = fpdec!(12.34);
let rate: FeeRate = fpdec!(0.001);

// `fee` inherits the type of `b`.
let fee = b * rate;
assert_eq!(fee, fpdec!(0.0123)); // loss precision

// If you want to check overflow, or want to specify new decimal type for
// the result, use `checked_mul()`:
type AnotherBalance = ConstScaleFpdec<i64, 8>; // longer precision
let fee: AnotherBalance = b.checked_mul(rate).unwrap();
assert_eq!(fee, fpdec!(0.01234));

// Multiplication operations can result in loss of precision. The default behavior
// is round, though custom rounding strategies are supported by `*_ext()` methods:
let fee: Balance = b.checked_mul_ext(rate, Rounding::Ceiling).unwrap();
assert_eq!(fee, fpdec!(0.0124));

// Also multiply by integer (but not float):
assert_eq!(b * 2, fpdec!(24.68));

Specify Scale

There are 2 ways to specify the scale: const and out-of-band:

• For the const type ConstScaleFpdec, we use Rust’s const generics to specify the scale. For example, ConstScaleFpdec<i64, 4> means scale is 4.

• For the out-of-band type OobScaleFpdec, we do NOT save the scale with decimal types, so it’s your job to save it somewhere and apply it in the following operations later. For example, OobScaleFpdec<i64> takes no scale information.

Generally, the const type is more convenient and suitable for most scenarios. For example, in traditional currency exchange, you can use ConstScaleFpdec<i64, 2> to represent balance, e.g. 1234.56 USD and 8888800.00 JPY. And use ConstScaleFpdec<u32, 6> to represent all market prices since 6-digit-scale is big enough for all currency pairs, e.g. 146.4730 JPY/USD and 0.006802 USD/JPY:

use primitive_fixed_point_decimal::{ConstScaleFpdec, fpdec};
type Balance = ConstScaleFpdec<i64, 2>; // 2 is enough for all currencies
type Price = ConstScaleFpdec<u32, 6>; // 6 is enough for all markets

let usd: Balance = fpdec!(1234.56);
let price: Price = fpdec!(146.4730);

let jpy: Balance = usd * price;
assert_eq!(jpy, fpdec!(180829.71));

However in some scenarios, such as in cryptocurrency exchange, the price differences across various markets are very significant. For example 81234.0 in BTC/USDT and 0.000004658 in PEPE/USDT. Here we need to select different scales for each market. So it’s the Out-of-band type:

use primitive_fixed_point_decimal::{OobScaleFpdec, fpdec};
type Balance = OobScaleFpdec<i64>; // no global scale set
type Price = OobScaleFpdec<u32>; // no global scale set

// each market has its own scale configuration
struct Market {
    base_asset_scale: i32,
    quote_asset_scale: i32,
    price_scale: i32,
}

// let's take BTC/USDT market as example
let btc_usdt = Market {
    base_asset_scale: 8,
    quote_asset_scale: 6,
    price_scale: 1,
};

// we need tell the scale to `fpdec!`
let btc: Balance = fpdec!(0.34, btc_usdt.base_asset_scale);
let price: Price = fpdec!(81234.0, btc_usdt.price_scale);

// we need tell the scale difference to `checked_mul()` method
let diff = btc_usdt.base_asset_scale + btc_usdt.price_scale - btc_usdt.quote_asset_scale;
let usdt = btc.checked_mul(price, diff).unwrap();
assert_eq!(usdt, fpdec!(27619.56, btc_usdt.quote_asset_scale));

Obviously it’s verbose to use, but offers greater flexibility.

In summary,

• if you know the scale (decimal precision) at compile time, choose ConstScaleFpdec;
• if you know it at runtime, choose OobScaleFpdec;
• if you have no idea about it (maybe because the scale is variable rather than fixed, e.g. in a general-purpose decimal math library), you need a floating-point decimal crate, such as bigdecimal or rust_decimal.

You can also use these two types in combination. For example, use OobScaleFpdec as Balance and ConstScaleFpdec as FeeRate.

Comparison

There are kinds of ways to represent fractions. This crate is fixed-point and decimal. So here we compare it with floating-point and binary.

Floating-point vs Fixed-point. For floating-point, the scale is stored in each instance and changes with calculations (hence the name “float”). As the scale changes, the range of representable values also changes. While this allows for a larger range, it can loss fraction precision and lead to round-off errors. In contrast, fixed-point ensures the fraction precision. Additionally, the instances in fixed-point only needs to store the significant digits, but no scale, resulting in higher memory utilization. For example, the 128 bits of the ConstScaleFpdec<i128, _> type in this crate are fully used to represent significant digits; by contrast, the Decimal type from rust_decimal also occupies 128 bits, but only has 96 bits significant digits.

Binary vs Decimal. Binary for machines, decimal for humans. Binary works well inside computer, but can not represent decimal fractions accurately. This leads to some odd issues of precisio when interacting with humans.

Here are some instances for each kinds:

• Floating-point Binary: primitive f32
• Floating-point Decimal: crate rust_decimal, bigdecimal, fastnum
• Fixed-point Binary: crate fixed
• Fixed-point Decimal: THIS crate primitive_fixed_point_decimal !!!

For example, in financial scenarios, it is essential to ensure the fraction precision and accurate representation. So the fixed-point decimal is the best choice.

However, even in finance, floating-point are more adopted than fixed-point. I think there are three reasons. 1. In most cases, the required representable range is small enough to avoid floating-point round-off errors. Here, they works as fixed-point actually; 2. In most cases, high memory utilization is not critical; 3. Floating-point is more convenient to use, you do not need to manually manage the precision of each type.

Additionally, some projects use neither floating-point nor fixed-point decimal crates, but only raw underlying integers and manual scale management. E.g., the BTC project uses integers for 1e-8 BTC units. Add and subtract via integer ops directly; while calculate fees by multiplying rate then dividing by scale manually.

Two extremes here:

• Floating-point decimal: simple and convenient, you do not need to concern for the precisions for each type. It’s like dynamic scripting languages.
• Raw underlying integer: straightforward but verbose, you have to manually manage the scale. It’s like assembly languages.

Fixed-point decimal, however, falls between these two extremes. It encapsulates underlying integers, manages the scale automatically, and offers safety and convenience without introducing any performance overhead. It’s like statically typed languages.

License

MIT

Macros

fpdec

Build decimal from integer or float number easily.

Structs

ConstScaleFpdec

Const-scale fixed-point decimal.

OobFmt

Wrapper to display/load OobScaleFpdec.

OobScaleFpdec

Out-of-band-scale fixed-point decimal.

Enums

ParseError

Error in converting from string.

Rounding

Rounding kinds.

Traits

FpdecInner

The trait for underlying representation.

IntoRatioInt

Used by method checked_mul_ratio() only.