Computer Work Calculator

This calculator has two uses:

1. You can determine the fair value of computing power on a commercial distributed computing network. Just enter the interest rate, the amount of months it takes for computing power per dollar to double, and the cost per gigaflop of the most cost-efficient computer available on the market. This will then tell you what the fair value of one quadrillion floating point operations is on a hypothetical distributed computing network, and the fair value of one year's worth of a CPU running at one gigaflop.

2. Given a certain amount of money, and a certain amount of instructions to execute, you can find the soonest possible time you can execute those instructions with that amount of money. For example, if you have $1,000 and want to decrypt a file that would take a gigaflop computer one million years, you can enter "1000" into the Cash field, and "1e6" into the Gigaflop Years field. If you left that $1,000 in a bank account, you would be able to purchase enough computing in 24.87 years to decrypt the file.

How This Works

When you purchase a CPU, you are purchasing all of the operations that CPU will execute over its lifespan. An operation performed in one year is worth less than one performed today, for two reasons. The most significant is that the cost of computing power is cut in half every 18 months, which amounts to a 1 - 2^(-12/18) = 37% drop every year. The second reason is simply that anything with value today can be put in a bank and collect interest over the next year. So, assuming an interest rate of 6%, something that costs one dollar today could be bought with 1 / 1.06 = 0.943 dollars if you wait a year while your money collects interest. Combine the two, and you get [2^(-12/18)] / 1.06 = 0.5943. One gigaflop a year from now is therefore worth 59.43% of the value of a gigaflop today. To the right is a chart of the output of a CPU, displaying the value of its computations as it ages.

The value of the CPU itself, then, is the sum of the value of each individual computation it performs in its lifespan. The formula governing the sum of a continuous sequence like this one is:

where r = the rate of change in the production of the CPU per year, calculated by [2^(-12/m)] / (1 + s), where m is the amount of months it takes for computing power per dollar to double, and s is the interest rate. Using the values above, r = 0.5943. So, the value, v, of a computer is:

where p equals the value of all the operations the computer will perform over the next year, if it performs them right now. In other words, p = the current yearly rate of production of the CPU. If you already know v, then you can therefore find p with the following formula:

So, if the cheapest gigaflop/second CPU costs $800, then the fair price of one gigaflop year of computing power = $800(log_e1/0.5943) = $416.29. To find the cost of a petaflop, you simply multiply that number by 2^20, and divide by the amount of seconds in a year, 86400 * 365.25.

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