Conventional techniques in energy-efficient computing navigate a design space defined by the two dimensions of performance and energy, and traditionally trade one for the other. General-purpose approximate computing explores a third dimension, error, and trades the accuracy of computation for gains in both energy and performance.
By relaxing the need for fully precise or completely deterministic operations, approximate computing techniques allow substantially improved energy efficiency. A team at the University of Illinois flagship campus recently published a paper that details how this technique can boost a bitcoin miners profits by 30%.
Led by Associate Professor of Electrical and Computer Engineering, Rakesh Kumar Ph.D., the three authors of “Approximate Bitcoin Mining” claim that the 6-page paper is the first to explore hardware optimizations, specifically approximation based optimizations, unique to Bitcoin mining.
“Mining is inherently error tolerant due to its embarrassingly parallel and probabilistic nature. We exploit this inherent tolerance to inaccuracy by proposing approximate mining circuits that trade off reliability with area and delay.”
– Approximate Bitcoin Mining
Approximation is not a new idea, and has been used in areas such as lossy compression and numeric computation. John von Neumann wrote a paper on it in 1956, “Probabilistic logic and the synthesis of reliable organisms from unreliable components.”
This new paper states that Bitcoin mining is intrinsically resilient to errors, “its parallel nature minimizes the propagation of errors, and Bitcoin’s distributed verification system detects and invalidates any potentially erroneous solutions.”
Using approximation, they illustrate a more efficient way to go about processing the SHA-256 hashing algorithm that Application-Specific Integrated Circuit (ASIC) chips use during the bitcoin mining process. ASIC chips are currently the most efficient hardware for mining Bitcoin.
“We propose approximation as a technique to reduce delay and area of Bitcoin mining circuits, thereby increasing profits.”
– Approximate Bitcoin Mining
To calculate profitability, the authors chose to test a commercial ASIC Bitmain BM1385. The chip has a hash rate of 38.8 Ghash/s and power consumption of 10.2 W at nominal frequency and voltage. The paper considered mining yield, hash rate, power consumption and cost of electricity.
Variations of three different approximate adders were also examined; Ripple-Carry Adder (RCA), Carry-Lookahead Adders (CLA), and Kogge-Stone Adder (KSA). As an important arithmetic module, the adder plays a key role in determining the speed and power consumption of a system.
The conclusion derived from the test is that a particular design of KSA, namely 16-bit KSA, can raise profits by 30%, “15% from functional approximation and 15% from operational approximation.”
The authors cautioned that there are many unsuitable approximate adder designs for Bitcoin mining, including 8-bit KSA, which would lead to an unprofitable hashing core error rate.
Security consultant Sergio Demián Lerner, prior to leading the development team at Rootstock, also described how SHA-256 ASICs can be faster using approximation, on his blog in 2015. Lerner suggested and discussed a different type of adder in detail, called a Carry-Reduced CLA adder (CR-CLA). He also mentioned KSA as a possible candidate. but admitted that he had “not yet attempted to analyze the resulting designs.”
“I have no idea if a reduced carry design will actually outperform a standard design considering additional factors, such as the availability of optimized off-the-shelf adders compared to a custom adder. However, I estimate that it can actually provide a speedup of about 5%.”
– Sergio Demián Lerner, Security Consultant
The Bitcoin mining network currently earns around US$1.5 million each day, a figure that includes the bitcoins mined and the transaction fees gathered by all miners, multiplied by the market price in US dollars.
The amount of total revenue a miner earns is far more heavily dependent on the price of a bitcoin. “When the price goes up, there’s more confidence in mining, and [mining equipment makers] go and design the next-generation chips,” BTCC chief executive officer Bobby Lee said in an interview with Bloomberg Business. However, ultimately profits are what miners and equipment makers seek.
“Miners are entirely profit motivated. First, profit from newly mined Bitcoin, and then later, profit from transaction fees.”
– Marc Andreessen, General Partner at Andreessen Horowitz
Mining income, when measured in relation to the hash rate, has been decreasing steadily as more petahashes come online at a faster pace than ever before.
There is no guarantee that bitcoin mining ASIC makers agree with University of Illinois’ researchers findings. However, if enough profit increase is proven and ASIC makers find it profitable to manufacture and sell the chips, miners will be thrust into another chapter of the arms race. The paper makes it clear that changing the mining software alone isn’t enough; hardware changes in the ASIC mining chips are required to realize these gains.