DEC64: Decimal Floating Point (2020)

https://www.crockford.com/dec64.html

by vinhnx • 9 months ago

77 56 9 months ago

mildred593• 9 months ago

Can't wait to have it in my language!

cozzyd2• 8 months ago

The memory savings from 32 bit or even 16 bit floats are definitely not pointless! Not to mention doubling simd throughput. Speaking of which, without simd support this certainly can't be used in a lot of applications. Definitely makes sense for financial calculations though.

pwdisswordfishy• 8 months ago

This seems optimized for fast integer operations. Except that if I only cared about integers, I'd use an actual integer type.

cozzyd2• 8 months ago

Well I suppose it might be preferable if javascript used this type...

sjrd• 8 months ago

JavaScript engines do optimize integers. They usually represent integers up to +-2^30 as integers and apply integer operations to them. But of course that's not observable.

sfoley• 8 months ago

Near the end of the article, under Motivation:

The BASIC language eliminated much of the complexity of FORTRAN by having a single number type. This simplified the programming model and avoided a class of errors caused by selection of the wrong type. The efficiencies that could have gained from having numerous number types proved to be insignificant.

DEC64 was specifically designed to be the only number type a language uses (not saying I agree, just explaining the rationale).

adamnew123456• 8 months ago

Languages for scientific computing like FORTRAN provided multiple floating point types such as REAL and DOUBLE PRECISION as well as INTEGER, often also in multiple sizes. This was to allow programmers to reduce program size and running time. This convention was adopted by later languages like C and Java. In modern systems, this sort of memory saving is pointless.

More than that, the idea that anyone would be confused about whether to use integer or floating-point types absolutely baffles me. Is this something anyone routinely has trouble with?

Ambiguity around type sizes I can understand. Make int expand as needed to contain its value with no truncation, as long as you keep i32 when size and wrapping does matter.

Ambiguity in precision I can understand. I'm not sure this admits of a clean solution beyond making decimal a built-in type that's as convenient (operator support is a must) and fast as possible.

But removing the int/float distinction seems crazy. Feel free to argue about the meaning of `[1,2,3][0.5]` in your language spec - defining that and defending the choice is a much bigger drag on everyone than either throwing an exception or disallowing it via the type system.

bux93• 8 months ago

People routinely have trouble picking ints for monetary amounts, leading to all kinds of lovely rounding errors.

PaulHoule• 8 months ago

There's something to say for languages like Python and Clojure were plain ordinary math might involve ordinary integers, arbitrary precision integers, floats or even rationals.

In grad school it was drilled into me to use floats instead of doubles wherever I could which cuts your memory consumption of big arrays in half. (It was odd that Intel chips in the 1990s were about the same speed for floats and doubles but all the RISC competitors had floats about twice the speed of doubles, something that Intel caught up with in the 2000s)

Old books on numerical analysis, particularly Foreman Acton's

https://www.amazon.com/Real-Computing-Made-Engineering-Calcu...

teach the art of how to formulate calculations to minimize the effect of rounding errors which resolves some of the need for deep precision. For that matter, modern neural networks use specialized formats like FP4 because these save memory and are effectively faster in SIMD.

---

Personally when it comes to general purpose programming languages I've watched a lot of people have experiences that lead them to thinking that "programming is not for them", I think

   >>> 0.1+0.2
   0.30000000000000004

is one of them. Accountants, for instance, expect certain invariants to be true and if they see some nonsense like

   >>> 0.1+0.2==0.3
   False

it is not unusual for them to refuse to work or leave the room or have a sit-down strike until you can present them numbers that respect the invariants. You have a lot of people who could be productive lay programmers and put their skills on wheels and if you are using the trash floats that we usually use instead of DEC64 you are hitting them in the face with pepper spray as soon as they start.

lifthrasiir• 8 months ago

Previously:

https://news.ycombinator.com/item?id=7365812 (2014, 187 comments)

https://news.ycombinator.com/item?id=10243011 (2015, 56 comments)

https://news.ycombinator.com/item?id=16513717 (2018, 78 comments)

https://news.ycombinator.com/item?id=20251750 (2019, 37 comments)

Also my past commentary about DEC64:

Most strikingly DEC64 doesn't do normalization, so comparison will be a nightmare (as you have to normalize in order to compare!). He tried to special-case integer-only arguments, which hides the fact that non-integer cases are much, much slower thanks to added branches and complexity. If DEC64 were going to be "the only number type" in future languages, it had to be much better than this.

indolering• 8 months ago

Wtf is up with the clown car that is floating point standards?

CoastalCoder• 8 months ago

Can you be more specific?

stephencanon• 8 months ago

IEEE 754 is a floating point standard. It has a few warts that would be nice to fix if we had tabula rasa, but on the whole is one of the most successful standards anywhere. It defines a set of binary and decimal types and operations that make defensible engineering tradeoffs and are used across all sorts of software and hardware with great effect. In the places where better choices might be made knowing what we know today, there are historical reasons why different choices were made in the past.

DEC64 is just some bullshit one dude made up, and has nothing to do with “floating-point standards.”

welferkj• 8 months ago

The set of real numbers is continuous and uncountably infinite. Any attempt to fit it into a discrete finite set necessarily requires severe tradeoffs. Different tradeoffs are desirable for different applications.

maxlybbert2• 8 months ago

Well, for one thing, IEEE-757 was a significant improvement on the vendor-specific ways of handling floating point that it replaced ( https://people.eecs.berkeley.edu/~wkahan/ieee754status/754st... ).

I wasn't a big fan of floating point until I worked with a former college professor who had taught astrophysics. When possible, he preferred to use respected libraries that would give accurate results fast. But when he had to implement things himself, he didn't always necessarily want the fastest or the most accurate implementation; he'd intentionally make and document the tradeoffs for his implementation. He could analyze an algorithm to estimate the accumulated units in the last place error ( https://en.wikipedia.org/wiki/Unit_in_the_last_place ), but he realized when that wasn't necessary.

rdtsc3• 8 months ago

How would fix the standards, or if your point is about having too many, which one would you choose as the _one_?

lambdaone• 8 months ago

If you want the job done properly, this already exists: https://en.wikipedia.org/wiki/Decimal128_floating-point_form...

mgaunard• 8 months ago

There are a bunch of different encodings for decimal floating-point. I fail to see how this is the standard that all languages are converging to.

IEEE754 normalizes two encodings, BID and DPD, for decimal32, decimal64 and decimal128 precision presets. This is neither of those.

Many libraries use an approach with a simple significand + exponent, similar to the article, but the representation is not standardized, some use full integral types for this rather than specific bits (C# uses 96+32, Python uses a tuple of arbitrary integers). It's essentially closer to fixed-point but with a variable exponent.

The representation from the article is definitely a fairly good compromise though, specifically if you're dealing with mostly-fixed-point data.

moron4hire• 8 months ago

I fail to see how this is the standard that all languages are converging to.

Yes, you are failing to see it because it's not there.

Crockford had a hot book amongst junior and amateur JavaScript developers 17 years ago. But he's never really been involved in any language standardization work. Even his self-described "invention" of JSON I wouldn't really call an invention and rather a discovery that one could send JS object literals instead of XML over the wire. This discovery also opened a new class of XSS exploits until browsers implemented JSON.parse.

So, when he says "DEC64 is intended to be the only number type in the next generation of application programming languages," it's just the same, old bloviation he has always employed in his writing.

gwbas1c• 8 months ago

I do think DEC64 has merit: Most of the time, I'd prefer to be able to reason about how non-integers are handled; and I just can't reason about traditional floating point.

Yes, Doug does bloviate quite a bit. (And when I asked him if there was a way to make callbacks in Node.js / Javascript simpler, he mocked me. A few years later, "await" was added to the language, which generally cleans up callback chains.)

ramses0• 8 months ago

He literally says he "discovered" it!?!?! https://nofluffjuststuff.com/blog/douglas_crockford/2008/01/...

...primary source: """I do not claim to have invented JSON. I claim only that I discovered it. It existed in nature. I identified it, gave it a name, and showed how it was useful. I never claimed to be the first to have discovered JSON. I made my discovery in the spring of 2001. There were other developers who were using it 2000."""

I see value in this semi-simplistic representation of DEC64, and to respond to a peer comment, consider "DEC64-norm", where non-normalized representations are "illegal" or must be tainted/tagged/parsed like UTF-8 before processing.

His other "useful" contribution which I lament not seeing anywhere else is "The Crockford Keyboard" another "near-discovery" of existing useful properties in an endemic standard (the English alphabet): https://www.crockford.com/keyboard.html

I really wish that the X-Box onscreen keyboard used this layout! You could imagine that if you could "hot-key" back to the left row (vowels), and have "tab-complete" (ie: shift-tab/tab) it could be a pretty comfortable typing experience compared to the existing "let's copy QWERTY(?!)".

...I feel him as a kindred spirit of pragmatism and complexity reduction (which necessarily) introduces more complexity since we live in a world where complicated things exist. Compared to IEEE floating point numbers, this DEC64 or "Number()" type seems like a breath of fresh air (apart from normalization, as mentioned!).

spacedcowboy• 8 months ago

Atari 8-bit basic used something pretty similar to this [1], except it did have normalization. It only had 10 BCD digits (5 bytes) and 2 digits (1 byte) for exponent, so more of a DEC48 but still… That was a loooong time ago…

It was slightly more logical to use BCD on the 6502 because it had a BCD maths mode [2], so primitive machine opcodes (ADC, SBC) could understand BCD and preserve carry, zero etc flags

[1] https://www.atarimax.com/freenet/freenet_material/5.8-BitCom...

[2] http://www.6502.org/tutorials/decimal_mode.html

shawn_w• 8 months ago

I was expecting something about floating point formats used by some DEC PDP series computer...

PopePompus• 8 months ago

Yes, DEC did use a non-IEEE floating point format at least through the VAX-11 era. I was fooled by the title too.

RustyRussell• 8 months ago

A goid friend of mine worked on decimal floating point for IBM Power chips (I think it was Power 7 which had hardware support).

Anyway, he insisted on calling it just "Decimal Floating". Because there was "no point".

sevensor2• 8 months ago

Hilarious and apt.

Either you want fixed point for your minimum unit of accounting or you want floating point because you’re doing math with big / small numbers and you can tolerate a certain amount of truncation. I have no idea what the application for floating point with a weird base is. Unacceptable for accounting, and physicists are smart enough to work in base 2.

nyrikki2• 8 months ago

Decimal128 has exact rounding of decimal rules and preserves trailing zeros.

I don’t think Decimal64 has the same features, but it has been a while.

But unless you hit the limits of 34 decimal digits of significand, Decimal128 will work for anything you would use fixed point for, but much faster if you have hardware support like on the IBM cpus or some of the sparc cpus from Japan.

OPAP Agg functions as an example are an application.

zokier• 8 months ago

I'm pretty confident that dfp is used for financial computation. Both because it has been pushed heavily by IBM (who certainly are very involved in financial industry) and because many papers describing dfp use financial applications as motivating example. For example this paper: https://speleotrove.com/decimal/IEEE-cowlishaw-arith16.pdf

This extensive use of decimal data suggested that it would be worthwhile to study how the data are used and how decimal arithmetic should be defined. These investigations showed that the nature of commercial computation has changed so that decimal floating-point arithmetic is now an advantage for many applications.
It also became apparent that the increasing use of decimal floating-point, both in programming languages and in application libraries, brought into question any assumption that decimal arithmetic is an insignificant part of commercial workloads.
Simple changes to existing benchmarks (which used incorrect binary approximations for financial computations) indicated that many applications, such as a typical Internet-based ‘warehouse’ application, may be spending 50% or more of their processing time in decimal arithmetic. Further, a new benchmark, designed to model an extreme case (a telephone company’s daily billing application), shows that the decimal processing overhead could reach over 90%

YesThatTom2• 8 months ago

If they reversed the order of the fields, you could sort them by just pretending they are int64’s.

Someone• 8 months ago

No you couldn’t, given “Normalization is not required”, so we have

    10³ × 9 < 10¹ × 100000

tgv2• 8 months ago

What's the point of saying that it is "very well suited to all applications that are concerned with money" and then write 3.6028797018963967E+143, which is obviously missing a few gigamultiplujillion.

jcarrano• 8 months ago

No point whatsoever. If you have to deal with money you never use floating point. Either use arbitrary precision, or integers with a sufficiently small base like blockchains do (which can be also though of as fixed point). Also you would never be multiplying two money value (there are no "square dollars").

dahart4• 8 months ago

It can precisely represent decimal fractions with 16 decimal places, which makes it very well suited to all applications that are concerned with money.

How many decimal places do people use for financial calculations in practice? Google search’s AI answer said 4, 6, or sometimes 8. Is that true for large financial institutions, like banks and hedge funds and governments and bitcoin exchanges?

I’ve heard lots of people saying floating point isn’t good for financial calculations, and I believe it. Would DEC64 actually be good for money if it has 16 base 10 digits, and if so, why? If you need 8 decimal places, you have 8 digits left, and start losing decimal places at around 100M of whatever currency you’re working with. I’m just guessing that working with large sums is exactly when you actually need more decimal places, no?

PaulKeeble4• 8 months ago

I hate to break the news but banks use floating point numbers all the time, for financial calculations. They shouldn't but they do and they use all sorts of tricks like alternate rounding schemes and some pretty deep knowledge of floats to try and keep the books roughly right. I have never seen a Money type nor anything like DEC64 in a real commercial system, its all floats or ints/longs for pennies.

rdtsc3• 8 months ago

Wonder if it depends on which side of banking: investments, accounting, clients side (web pages, and ui) vs the backend. Or if we're talking about central banks vs a small credit union.

dahart4• 8 months ago

That’s not too surprising to me, I imagine that many number types are used, and it depends entirely on the task at hand? If you have deeper knowledge of what gets done in practice, I’m still curious what criteria and types and how many decimal points might get used in the most restrictive cases. What do people use in practice for, say, interest compounding on a trillion dollars? I can calculate how many decimal places I need at a minimum for any given transaction to guarantee the correct pennies value, but I don’t have first-hand experience with banks and I don’t know what the rules of thumb, or formal standards might be for safe & careful calculation on large sums of money. I would imagine they avoid doing floating point analysis in every case, since that’s expensive engineering?

jcranmer4• 8 months ago

The noob-expert meme is really apropos here, as floating-point is really the option to go for if you know nothing about it or you know a lot about it.

The "problem" with floating-point is that you have to deal with rounding. But in financial contracts, you have to deal with rounding modes. Fixed-point (aka integers) gives you one rounding mode, and that rounding mode is wrong.

RaftPeople• 8 months ago

I have never seen a Money type nor anything like DEC64 in a real commercial system, its all floats or ints/longs for pennies.

I've been working in ERP land for a long time working with many different commercial systems of different sizes and market share and I've only seen NUMERIC/DECIMAL types used in DB for things like Price, Cost, Amount etc.

The only time I've ever seen floating point is for storage of non-money type values, like latitude and longitude of store locations.

Examples of a few top systems:

SAP - Packed decimal

Oracle NetSuite - Decimal

Microsoft Dynamics - Decimal/Numeric

Infor - Decimal/Numeric

drob518• 8 months ago

Typically, you select a precision that you’re comfortable with and then use fixed point for everything. My broker seems to use 6 decimal places.

dmitrygr• 8 months ago

nan is equal to itself
The result of division by zero is nan

This is all a mistake!! IEEE put a lot of thought into making NaN != NaN and having Inf and NaN be separate things. As it stands 1e130 / 1e-10 == 5 / 0 == 0 / 0. Should that be the case? No. Why might this come up accidentally without you noting this? Imagine each of the following funcs is in a separate module written by separate people. frob() will be called errorneously with DEC64 and will not with float or double

   int main(int, char**) {

      //[...]

      rateOfThisThing = getRateOfThing1();
      rateOfThatThing = getRateOfThing2();

      if (rateOfThisThing == rateOfThatThing) {
         frob();
      }

      //[...]
   }

   void frob(void) {
      //[...]
   }

   DEC64 getRateOfThing1(void) {
       return calculateRate(mThingOneProgress, getTime() - mTimeWhenThing1started);
   }

   DEC64 getRateOfThing3(void) {
       return calculateRate(mThingTwoDone, getThingTwoRuningLength());
   }

   DEC64 calculateRate(DEC64 done, DEC64 time) {
       return (done + time / 2) / time
   }

DEC64: Decimal Floating Point (2020)

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