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Fractional amounts

Introduction: token decimals

If you know how token decimals work, feel free to skip this section.

We, the web3 users, are familiar with the notion of tokens being dividable into smaller parts. E.g. you can have 2.5 USDC, or you can receive 0.03 Ether. This in fact is not how the tokens are handled by the computers and the blockchains. The reality is that the tokens are indivisible, but all the quantities are much larger than what's presented to us, which enables the creation of an illusion of fractions. Every token has defined a number of decimals, in the case of USDC it's 6, in the case of Ether 18, and so on. The number of decimals is applied when displaying the amounts for the users. E.g. if your wallet states that you have 2.5 USDC, the actual amount stored in the smart contract has 6 extra digits and is 2,500,000 (2.5 * 10 ^ 6). When you want to transfer 0.003 Ether, the wallet sends in the transaction an amount with 18 extra digits, or in this case 30,000,000,000,000,000 (0.03 * 10 ^ 18). This convention makes handling tokens simpler for computers because they don't need to work with fractions. On the other hand for the users, the visible amounts are easy to work with, because they are small, have relatively high per-unit monetary value, and offer convenient fractions.

Language used in this section

This page uses the term "token unit" when talking about tokens as seen by the smart contract. For example, 0.000,001 USDC or 10 ^ -18 Ether (1 Wei) are both token units. Token units are not dividable into smaller parts, their amounts are expressed with integers.

Streaming rate has a sub-token precision

When setting up streams, each receiver is configured with an integer per-second streaming rate, amtPerSec. This rate is expressed in token units with 9 extra decimals, which lets express rates with precision higher than 1 token unit per second.

For example, the user wants to stream 0.000,001 USDC per second. USDC has 6 decimals, so the actual rate they want is 1 token unit per second. The streams configuration requires the rate to have 9 extra decimals, so the amtPerSec needs to be set to value 1,000,000,000. Streaming 0.000,001 USDC per second adds up to 2.592 USDC per 30 days. Let's say that the user feels that it's too much, now they want to stream only 1 USDC per 30 days. This is 0.385,802,469 token units per second, to which we add 9 decimals and end up passing as amtPerSec the integer value 385,802,469.

Example token amount representation
Tokens seen by the user0.05 USDC
Token units handled by smart contracts50,000 (USDC has 6 decimals, so we calculate 0.05 * 10 ^ 6)
Passed as amtPerSec as a per second streaming rate50,000,000,000,000 (amtPerSec requires adding 9 extra decimals to the number of token units, so we calculate 50,000 * 10 ^ 9)

The API requires 9 extra decimals only in StreamConfig's amtPerSec

In the Drips API per-second rates are always wrapped in StreamConfig packed structures, they are never passed or emitted as standalone integers. All instances of StreamConfig have their amtPerSec expressed as token units with 9 extra decimals. On the other hand, no other values follow that convention, all the balances and amounts are always expressed as regular numbers of whole token units without any extra precision or fractions.

Streamed amounts are always whole token units

When streaming, both the sender's balance and the amounts receivable by the receivers are always whole token units, and at all times they add up to the amount put into the protocol by the sender. There are no losses or temporarily stuck token units, the protocol is precise and sound when handling assets. This holds even when streaming at rates that are not expressible as whole token units per second. Partially streamed token units are kept in the sender's balance, but as soon as they add up to whole units, they're moved from the sender and become receivable by the receiver. This makes the amounts actually streamed on each timestamp change from second to second within a range of 1 token unit per second, but when observed over a period of time, the streamed token units add up to the rate which was configured.

For example, the user wants to stream 0.000,001,4 USDC per second, which is 1.4 token units per second. The streamed amount on the first second will be 1.4, so only 1 token unit will be subtracted from the sender's balance and moved to the receiver, 0.4 will stay on the sender's side. During the next second, another 1.4 token units are being streamed, to which 0.4 from the previous second is added resulting in 1.8 token units sent. Again 1 is moved from the sender to the receiver and 0.8 stays on the sender. Finally, during the third second, another 1.4 is streamed, which with 0.8 from the previous cycles adds up to 2.2. This time 2 token units are taken from the sender's balance and made receivable by the receiver, and 0.2 stays on the sender's side waiting to be streamed during the upcoming seconds.

Technical details of how streamed fractions add up

When streaming with a given rate the Nth second of each cycle moves the same amount from the sender to the receiver. It doesn't matter when streaming starts or ends, the exact amount streamed during a given second depends only on the rate and the position of the timestamp in the cycle. The first second of each cycle always moves floor(amtPerSec), but every other timestamp T moves floor(T % cycleSecs * amtPerSec) - floor((T - 1) % cycleSecs * amtPerSec).

The result of this behavior is that operations that update streams without altering the streaming rate, for example, a change of the balance, do not disrupt the existing streams. This makes calculating the amount streamed over a given period of time easy to do using just the rate and the cycle length.

Unfortunately, it may lead to surprising behaviors when streaming at extremely low rates. For example, a user streams 0.001 token units per second, so a single token unit should be moved to the receiver once every 1000 seconds. Depending on when exactly streaming starts, a token unit may be moved on the first second of streaming or it may be moved after 999 seconds, to the user it may look random. Consecutive token units will be moved as expected, once per 1000 seconds. The only exception is when a cycle ends, because then the unmoved fractions will be cleared, and the countdown to moving the next token unit will be reset to 1000 seconds.

The cycle boundaries behavior determines the lowest possible streaming rate, which is 1 token unit per cycle. If a streaming rate is lower than that, a stream configuration is invalid, because it would cause no movement of tokens. The minimum valid amount per second of 1 token unit per cycle is exposed by the Drips contract as minAmtPerSec.