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Fast, fixed-size, floating-point decimal types.

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Fast, fixed-size, floating-point decimal types.

This crate represents decimals accurately by scaling integer in base-10.
So there is no round-off error like 0.1 + 0.2 != 0.3.

There are kinds of ways to represent decimals, each with its own focus.
This crate is same kind to the most popular [`rust_decimal`](https://docs.rs/rust_decimal),
but *better*.

# Compare with `rust_decimal`

This crate has these advantages:

- Much faster. This crate is 2X ~ 6X faster than `rust_decimal` at `+`, `-`
and `*` operations. While the `/` is complex, with both faster and slower
cases. A typical comparison is shown in below chart. See
the [benchmark](https://github.com/WuBingzheng/decimax/blob/v0.2.0/benches/README.md)
for details.

![Benchmark result](https://raw.githubusercontent.com/WuBingzheng/decimax/refs/tags/v0.2.0/benches/charts/mul-amd.svg)

- More significant digits and fraction digits. All bits of the underlying
integer are used. No waste. For example the 128-bit signed decimal type
[`Dec128`] has 122 bits for mantissa (about 36 decimal significant digits),
5 bits for scale (at most 31 fraction digits), and 1 bit for sign. While
`rust_decimal` has 96 bits for mantissa (about 28 digits) and at most
28 fraction digits.

- More types. It provides [6 types](#types) by now. Long and short (128/64/32-bit),
signed and unsigned.

# How is it made faster?

In fact, there is no black magic in this crate (except for a fast division
algorithm which is used in just a few cases). I suspect the performance gain
isn’t so much because this crate is fast, but because `rust_decimal` is slow.

In this crate, the decimal is defined as a single integer. Take the 128-bit type
as example:

```text
+-+-----+-------------------------------+
|S|scale|  mantissa                     |
+-+-----+-------------------------------+
```

The sign(`S`), scale, and mantissa occupy 1, 5, and 122 bits respectively.
The mantissa is computed as one single `u128` integer for each operation.

In contrast, the definition in `rust_decimal` is as follows:

```text
+---------+---------+---------+---------+
| flags   | high    | mid     | low     |
+---------+---------+---------+---------+
```

The mantissa consists of three `u32` components, and each operation requires
processing these three `u32` values in turn. Additionally, `rust_decimal`
checks whether the two operands are small(32 bit), medium(64 bit), or
large(96 bit), and uses different computation processes accordingly.
These conditional checks themselves, along with the complex logic, may
slow down the arithmetic operations.

You’ll get my point as long as you take a quick look at the code of the
addition implementation
[of this crate](https://docs.rs/crate/decimax/0.2.0/source/src/ops.rs#32)
and [of rust_decimal](https://docs.rs/crate/rust_decimal/1.41.0/source/src/ops/add.rs).

In [`rust_decimal`'s documentation](https://docs.rs/rust_decimal/1.41.0/rust_decimal/#comparison-to-other-decimal-implementations),
it's said that:

>  This structure allows us to make use of algorithmic optimizations to implement
>  basic arithmetic; ultimately this gives us the ability to squeeze out performance
>  and make it one of the fastest implementations available.

I don't quite understand this sentence. I have to guess that it was developed
before Rust's `u128` type was stabilized, when only `u64` or `u32` could be used.

I’m not a performance expert, so the above is just my speculation. However,
the [benchmark results](https://github.com/WuBingzheng/decimax/blob/v0.2.0/benches/README.md)
are objective. Please check it out and run it yourself.

# Usage

```rust
// We take the 128-bit type as example.
use decimax::{Dec128, UDec32};
use core::str::FromStr;

// Construct from integer, float, or string.
let a = Dec128::from(123);
let b = Dec128::try_from(123.456).unwrap();
let c = Dec128::from_str("123.456").unwrap();

// Construct from mantissa and scale. This is low level.
let b2 = Dec128::from_parts(123456, 3);
assert_eq!(b, b2);

// Addition and substraction operate with same type only.
assert_eq!(a + b, Dec128::from_parts(246456, 3)); // 123 + 123.456 = 246.456

// Multiplication and division can operate with short integers and decimals too.
let p = Dec128::from_parts(246912, 3); // 123.456 * 2 = 246.912
assert_eq!(b * 2, p); // by integer
assert_eq!(b * UDec32::from_parts(2, 0), p); // by new unsigned decimal type
```

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