Ecma TC39 JavaScript Decimal proposal

The TC39 Decimal proposal is an investigation into adding a built-in data type in JavaScript to represent base-10 decimal numbers.

This whole proposal is basically a big open question, and we'd welcome your participation in discussing the design space in the issues linked above. We are seeking input for your needs around JavaScript decimal in this survey.

Champions: Daniel Ehrenberg (Igalia), Andrew Paprocki (Bloomberg)

Stage: Stage 1 of the TC39 process.

Use cases and goals

Accurate storage and processing of base-10 decimal numbers is a frequent need in JavaScript. Currently, developers sometimes represent these using libraries for this purpose, or sometimes use Strings. Sadly, JavaScript Numbers are also sometimes used, leading to real, end-user-visible rounding errors.

The goal of the Decimal proposal is to add a decimal type to the JavaScript standard library, in a way that provides such good ergonomics, functionality and performance that people feel comfortable using it when it's appropriate. Being built-in to JavaScript means that we will get optimizable, well-maintained implementations that don't require transmitting, storing or parsing additional JavaScript code.

Primary use case: Representing human-readable decimal values such as money

Many currencies tend to be expressed with decimal quantities. Although it's possible represent money as integer "cents", this approach runs into a couple issues:

• There's a persistent mismatch between the way humans think about money and the way it's manipulated in the program, causing mental overhead for the programmer.
• Different currencies use different numbers of decimal positions which is easy to get confused. (It's not correct to assume that all currencies have two decimal places, or that the only exception is JPY; making such assumptions will make it hard to internationalize your code to new countries.) For this reason, it's ideal if the number of decimal places is part of the data type.
• In various contexts (e.g., presenting the quantity to the end user), the fractionality needs to be brought back in somehow. For example, Intl.NumberFormat only knows how to format Numbers, and can't deal with an integer + exponent pair.
• Sometimes, fractional cents need to be represented too (e.g., as precise prices).

Sample code

For example, to add up a bill with a number of items, and add sales tax, the BigDecimal alternative (described below) could allow the following:

function calculateBill(items, tax) {
  let total = 0m;
  for (let {price, count} of items) {
    total += price * BigDecimal(count);
  }
  return BigDecimal.round(total * (1m + tax),
                          {maximumFractionDigits: 2, round: "up"});
}

let items = [{price: 1.25m, count: 5}, {price: 5m, count: 1}];
let tax = .0735m;
console.log(calculateBill(items, tax));

Why use JavaScript for this case?

Historically, JavaScript may not have been considered a language where these representations and manipulations are necessary. In some application architectures, JS only deals with a string representing a human-readable decimal quantity, and never do calculations or conversions. However, several trends push towards JS's deeper involvement in with decimal quantities:

• More complicated frontend architectures: Rounding, localization or other presentational aspects may be performed on the frontend for better interactive performance
• Serverless: Many Serverless systems use JavaScript as a programming language in order to better leverage the knowledge of frontend engineers
• Server-side programming in JavaScript: Systems like Node.js and Deno have grown in popularity to do more traditional server-side programming in JavaScript

In all of these environments, the lack of Decimal support means that various workarounds have to be used:

• An external library could be used instead (introducing issues about choosing the library, coordinating on its use)
• Calculations could be in terms of "cents" (fallible as explained above)
• In some cases, developers end up using Number instead, believing it to be mostly safe, but in practice causing bugs

Goals implied by use case

This use case implies the following goals:

• Avoid unintentional rounding that causes user-visible errors
• Basic mathematical functions such as +, -, *
• Sufficient precision for typical money/human-readable quantities
• Rounding facilities including parameters for both precision and rounding mode
• Ability to divide a Decimal quantity roughly equally into an integer number of groups
• Conversion to string, in a locale-sensitive manner
• Sufficient ergonomics to enable correct usage
• Be implementable with adequate performance/memory usage for applications
• Avoid confusing parts of floating point, e.g., -0, NaN, infinity--exceptions make sense for business computing
• (Please file an issue to mention more requirements)

Secondary use case: Numerical calculations on more precise floats

If it works out reasonably to provide for it within the same proposal, it would also be nice to provide support for higher-precision applications of floating point numbers.

If Decimal is arbitrary-precision or supports greater precision than Number, it may also be used for applications which need very large floating point numbers, such as astronomical calculations, physics, or even certain games. In some sense, larger or arbitrary-precision binary floats (as supported by QuickJS, or IEEE 754 128-bit/256-bit binary floats) may be more efficient, but Decimal may also be suitable.

Sample code

For example, Fabrice Bellard wrote this code to calculate digits of pi using BigDecimal.

Why use JavaScript for this case?

(TODO)

Goals implied by use case

This use case implies the following goals:

• Basic mathematical functions such as +, -, *
• Support of various numerical functions (e.g., trigonometric, log/exp, etc)
• Sufficient precision for these applications (unclear how high--would require more analysis of applications)
• Be implementable with adequate performance/memory usage for applications
• -0, NaN, infinities may be useful here, rather than exceptions, to continue work in exceptional conditions
• (Please file an issue to mention more requirements)

Cross-cutting: Interaction with other systems using decimals

If Decimal becomes a part of standard JavaScript, it may be used in some built-in APIs in host environments:

• For the Web platform: (#4)
  • HTML serialization would support Decimal, just as it supports BigInt, so Decimal could be used in postMessage, IndexedDB, etc.
  • In WebPayments, the transaction amount is generally represented as a string. Although strings will need to be used forever in JSON contexts, some APIs may also introduce a way to be used with Decimal.
• For WebAssembly, if WebAssembly adds IEEE 64-bit and/or 128-bit decimal scalar types some day, then the WebAssembly/JS API could introduce conversions along the boundary, analogous to WebAssembly BigInt/i64 integration

More host API interactions are discussed in #5.

JavaScript is also used to communicate with external systems, such as databases and foreign function interfaces to other programming languages.

Why use JavaScript for this case?

JavaScript is frequently used as a language to glue other systems together, whether in client, server or embedded applications. Its ease of programming and embedding, and ubiquity, lend itself to this sort of use case. Programmers often don't have the option to choose another language. When decimals appear in these contexts, it adds more burden on the embedder to develop an application-specific way to handle things; such specificity makes things less composable

Goals implied by the use case

Interaction with other systems brings the following requirements:

• Ability to round-trip decimal quantities from other systems
• Serialization and deserialization in standard decimal formats, e.g., IEEE 754's multiple formats
• Precision sufficient for the applications on the other side

Language design goals

In addition to the goals which come directly from use cases mentioned above,

• Well-defined semantics, with the same result regardless of which implementation and context a piece of code is run in
• Build a consistent story for numerics in JavaScript together with Numbers, BigInt, operator overloading, and potential future built-in numeric types
• No global mutable state involved in operator semantics; dynamically scoped state also discouraged
• Ability to be implemented across all JavaScript environment (e.g., embedded, server, browser)

Early draft syntax and semantics: Investigation with multiple paths

With this proposal at Stage 1, details aren't nailed down. However, for concreteness, some initial possible details are provided below. You're encouraged to join the discussion by commenting on the issues linked below or filing your own.

This proposal is still in early stages, so we are investigating two possible paths: BigDecimal and Decimal128. Below we describe some important elements for each path we are investigating. Much of the syntax and semantics is the same between these different paths, so the common elements are represented first. We have a more detailed documentation of each proposal on decimal128-reference.md and bigdecimal-reference.md.

Common elements

Decimal is generally analogous to BigInt, complete with:

• Literal syntax: 123.456m is a BigDecimal/Decimal128 value (#7)
• Operator overloading: .1m + .2m === .3m

Data model:

• Decimal represents a mathematical, "normalized" (#26) base 10 decimal
  • For example, 2m is exactly the same value as 2.00m (#11)
  • If preserving magnitude/precision through trailing zeroes is required, it needs to be represented separately from the Decimal
  • There is no Infinity, -0, NaN, etc; error cases lead to exceptions, just like BigInt, and -0m is 0m (#9)
• A new primitive type, not an object: typeof 1m === "bigdecimal" (or "decimal128")
  • There can still be methods on BigDecimal.prototype/Decimal128.prototype due to the magic of wrappers, just like Number.

Operator semantics:

• The operators +, -, *, % are defined.
• Bitwise operators are not supported, as they don't logically make sense on the Decimal domain (#20)
• Use explicit casts when you need to do a calculation involving different numerical types. Otherwise, a TypeError is thrown, like for BigInt+Number. (#10)
• Comparison with === compares two Decimals for mathematical equality, and returns false if comparison is with another type; comparison with ==, <, etc can compare Decimal with any numerical type.

Decimal methods for calculation: (#14)

• BigDecimal/Decimal128.round(decimal, options) rounds a Decimal, based on an options bag with the following parameters:
  • options.roundingMode: Rounding mode, with exact set of values TBD, maybe including "up", "down", "half-up", "half-down", "half-even" (more?). There is no default; this must be explicitly provided
  • Exactly one of the two following options is required to indicate the precision to round to (names matching Intl.NumberFormat):
    • options.maximumFractionDigits: The maximum number of decimal places after the .
    • options.maximumSignificantDigits: The maximum number of significant digits
• BigDecimal/Decimal128.div(a, b, options), and similarly for add, sub and mul: Takes three parameters: two Decimal and a rounding mode
  • E.g., BigDecimal/Decimal128.div(1m, 3m, { maximumFractionDigits: 2, roundingMode: "down" }) === .33m
• BigDecimal/Decimal128.pow(decimal, number, options) only supports positive integer exponents. The operator form of ** is not available.
• BigDecimal/Decimal128.partition(decimal, pieces, roundingOptions) returns an Array of length pieces with the Decimal split as evenly as possible, based on the rounding options which indicate precision
• [Big]Decimal64Array and [Big]Decimal128Array (binary format implementation-defined to be one of the two IEEE formats, and then dataview methods take flag; (#16)). Even if Decimal128 is used, writing a Decimal128 into a TypedArray would not reveal the number of trailing zeroes.

The library of numerical functions here is deliberately minimal. It is based around targeting the primary use case. For the secondary use case of numerical computations, developers may experiment in JavaScript, developing such libraries, and we may decide to standardize these functions in a follow-on proposal.

BigDecimal methods for string formatting:

• BigDecimal/Decimal128.prototype.toString() is similar to the behavior on Number, e.g., 123.456m.toString() is "123.456". (#12)
• toFixed, toExponential, toPrecision methods analogous to Number methods
• Intl.NumberFormat.prototype.format transparently supports Decimal (#15)
  • Intl.NumberFormat is extended to take a roundingMode option, which works on all numeric types

The main difference between the two proposals below is the data model of decimals: unlimited precision vs IEEE 754-2008 128-bit decimal. This is a tradeoff with advantages and disadvantages on either side. Further discussion of this tradeoff is in #8.

Option: BigDecimal

Data model: Unlimited size decimals, represented exactly as mathematical values.

Operators +, -, *, % always calculate their exact answer. In particular, if two BigDecimals are multiplied, the precision of the result may be up to the sum of the operands. For this reason, BigDecimal.pow takes a mandatory options object, to ensure that the result does not go out of control in precision.

The operator / is not available on BigDecimals because a rounding parameter is required. Instead, use BigDecimal.div function, where the options are mandatory. (The options are optional for, e.g., BigDecimal.add, since there is always an exact answer.)

See #13 for further discussion of division in BigDecimal.

Option: Decimal128

Data model: IEEE 754-2008/2019 128-bit decimal, normalized. IEEE 754 decimal can represent trailing zeroes, but these are not made visible/available to JavaScript.

Operators +, -, * and / may all round, with certain operands, if they run into the limits of precision in IEEE decimal. These limits are rather large and unlikely to occur in realistic calculations involving money or other human-intelligible quantities. The default rounding mode is half-even, as with Numbers.

The Decimal128.add/div/etc methods might or might not be omitted in this case; if they are included, the options are never required.

Plan going forward: Prototype both paths

From the champion group's perspective, both BigDecimal and Decimal128 are both coherent, valid proposals that would meet the needs of the primary use case. Just looking at the diversity of semantics in other programming languages, and the lack of practical issues that programmers run into, shows us that there are many workable answers here.

We're aware that there are delegates in TC39 who prefer one or the other path. We'd like to collect broader feedback based on realistic usage of these alternatives. We intend to do the following to test both alternatives:

• For each, develop a speculative polyfill implementations, along the lines of JSBI, which could also be used with the operator overloading transform
• Write strong documentation, sample code, cookbook, etc for both alternatives
• Request feedback from the JavaScript community in using the alternatives

Due to these complicated design questions, as well as interaction with other proposals (especially operator overloading), the champions do not expect Decimal to move as quickly through TC39's process as BigInt did. Stage 2 at the end of 2020 would be an optimistic estimate if all goes very well. Stage 2 would require having reached a conclusion on the question of BigDecimal vs Decimal128.

FAQ

Why are literals m? Why not d?

As with BigInt, there's not a huge amount of precedent from other programming languages about a literal suffix. Newer languages in the .NET ecosystem tend to use m, but outside of that family, few languages use a suffix to indicate decimal literals. So there isn't a lot of precedent to go on.

Many people have raised the idea that we use d as the suffix for decimal. It is the first letter! However, thinking about this further, it would not extend to hexadecimal literals, which may include d.

Although this proposal does not include hexadecimal syntax for decimals, it would be ideal to work with a syntax that could be extended to them, or even to "explain" the decimal syntax in terms of a generalized extended numeric literals proposal (which would necessarily support hexadecimal literals, to explain BigInt).

Would fractions/rationals meet these use cases?

Fractions would be an interesting thing to pursue in TC39, and are in many ways complementary to Decimal. Many languages in the Lisp tradition include fractions of arbitrary-size integers as a basic data type, alongside IEEE-754 64-bit binary floating point numbers; Ruby and Python also include fractions in their standard library.

We see fractions as complementary to Decimal because of a mismatch when it comes to two of the core operations on Decimals:

• Rounding to a certain base-10 precision, with a rounding mode
• Conversion to a localized, human-readable string

These could be defined on rationals, but are a bit of an inherent mismatch since rationals are not base 10.

Two further issues:

• Efficiency: Simple operations like addition of fractions requires use of a greatest-common-denominator (GCD) algorithm to normalize the fraction. At the same time, even with that, the denominator can get pretty big with just a few operations if care isn't taken. (BigDecimal may get rather large due to repeated multiplication, but fractions face this issue with simple addition and subtraction as well.)
• Still limited expressiveness: Rationals still cannot express most polynomial or trigonometric values, so the exactness benefits still fall away in most cases. It's not clear how often practical programs actually need preciseness in fractions but not those other issues. It certainly comes up sometimes, though.

Rational may still make sense as a separate data type, alongside Decimal. Further discussion of rationals in #6.

Will Decimal have good performance?

This depends on implementations. Like BigInt, implementers may decide whether or not to optimize it, and what scenarios to optimize for. We believe that, with either alternative, it is possible to create a high-performance Decimal implementation. It may be somewhat more complicated to do so for BigDecimal than for Decimal128. Historically, faced with a similar decision of BigInt vs Int64, TC39 decided on BigInt; such a decision might not map perfectly because of differences in the use cases. Further discussion: #27

Will Decimal have the same behavior across implementations and environments?

One option that's raised is allowing for greater precision in more capable environments. However, Decimal is all about avoiding unintended rounding. If rounding behavior depended on the environment, the goal would be compromised in those environments. Instead, this proposal attempts to find a single set of semantics that can be applied globally.

How does this proposal relate to decimal in the JS ecosystem and other programming languages and systems?

See COMPARISON.md for details.

How does this proposal relate to other TC39 proposals like operator overloading?

See RELATED.md for details.

Why not have the maximum precision or default rounding mode set by the environment?

Many decimal implementations support a global option to set the maximum precision (e.g., Python, Ruby). In QuickJS, there is a "dynamically scoped" version of this: the setPrec method changes the maximum precision while a particular function is running, re-setting it after it returns. Default rounding modes could be set similarly.

Although the dynamic scoping version is a bit more contained, both versions are anti-modular: Code does not exist with independent behavior, but rather behavior that is dependent on the surrounding code that calls it. A reliable library would have to always set the precision around it.

There is further complexity when it comes to JavaScript's multiple globals/Realms: a Decimal primitive value does not relate to anything global, so it would be inviable to store the state there. It would have to be across all the Decimals in the system. But then, this forms a cross-realm communication channel.

Therefore, this proposal does not contain any options to set the precision from the environment.

Where can I learn more about decimals in general?

Mike Cowlishaw's excellent Decimal FAQ explains many of the core design principles for decimal data types, which this proposal attempts to follow.

One notable exception is supporting trailing zeroes: Although Mike presents some interesting use cases, the Decimal champion group does not see these as being worth the complexity both for JS developers and implementers. Instead, Decimal values could be lossly represented as rationals, and are "normalized".

TC39 meeting notes

• November 2017; slides

Implementations

• Experimental implementation in QuickJS, from release 2020-01-05 (use the --bignum flag)
• We are looking for volunteers for the following implementation tasks:
  • Writing a polyfill along the lines of JSBI for both alternatives, see #17
  • Implementing Decimal syntax (but no transform) in a Babel PR, see #18

Getting involved in this proposal

Your help would be really appreciated in this proposal! There are lots of ways to get involved:

• Share your thoughts on the issue tracker
• Document your use cases, and write sample code with decimal, sharing it in an issue
• Research how decimals are used in the JS ecosystem today, and document what works and what doesn't, in an issue
• Help us write and improve documentation, tests, and prototype implementations

See a full list of to-do tasks at #45.