## PSI Technology & Interactive Simulation

With Risk Solver, risk analysis for uncertain models becomes as easy as asking 'what if'. With **Interactive Simulation**, each time you change a number on the spreadsheet, a **simulation with thousands of trials** is performed -- often in no more time than a single spreadsheet recalculation -- and a full range of simulation results and statistics can be displayed. Suddenly, you find that insights about the model, and decisions you can make, start to flow intuitively. Early users have called this instant, interactive feedback **"addictive."** In Dr. Sam Savage's words,

“Risk Solver Engine does for uncertainty what the spreadsheet did for numbers.”

But there is a deeper advantage of Interactive Simulation: It gives you a *new way to think about your model*. The key step in risk analysis -- versus conventional spreadsheet 'what-if' analysis -- is to **think in terms of a range of scenarios**, considered at once. With Interactive Simulation, you can begin to think of each worksheet cell as representing not just a single number, but an *array* of numbers that covers the full range of possibilities.

*Incredible Simulation Speed with PSI Technology™*

*Incredible Simulation Speed with PSI Technology™*

Risk Solver implements Interactive Simulation using Frontline's PSI Technology™. You create an ordinary 'what-if' spreadsheet model, with cells and formulas to compute the results you need -- for *just one scenario*. Risk Solver does the rest -- and it computes Monte Carlo trials up to **100 times faster** than using Excel alone. PSI Technology is fast enough to make Interactive Simulation *practical* for realistic simulation models.

#### Vectorized Evaluation

So, how does PSI Technology work, and how can it be so much faster than Excel alone for simulation? To answer this, we must look at how Excel itself computes values for your formulas. Microsoft Excel is an *interpreter* for spreadsheet formulas.

When you enter a formula such as =A1+A2*(A3-4) in cell B1, Excel first scans and *parses* the formula, storing the results in a coded internal form. It also maintains storage for A1, A2, A3 and thousands of other cells. When you change a number and recalculate, Excel refers to the coded internal form, looks up the values of A1, A2 and A3 and fetches the constant 4, performs the arithmetic, and saves the result in storage reserved for B1. *Only a small part of the time is spent on the actual arithmetic* -- most of the time goes into processing the encoded formula, and looking up and saving cell values.

PSI stands for ** Polymorphic Spreadsheet Interpreter**. PSI Technology is also an

*interpreter*for spreadsheet formulas, that accepts the same formula syntax and built-in functions as Microsoft Excel. But where Excel evaluates formulas only for one datatype - single numbers, PSI Technology can evaluate formulas for many different datatypes. (The word

**'polymorphic'**comes from object-oriented programming, where it has essentially the same meaning.)

One of the special PSI Technology datatypes is **Monte Carlo trials**, where each number is replaced by a **vector** of 1,000 or more trial values. The heart of PSI Technology's speed comes from the fact that it processes the encoded formula *once*, fetches 1,000 data values *at once*, and performs the arithmetic for all 1,000 values *at once*. Hence, the 'overhead' of the interpreter is incurred once rather than 1,000 times; *most of the time is spent doing the actual arithmetic*. This is called ** vectorized evaluation**. PSI Technology is so fast because it is

*specialized*for simulation.

PSI Technology also plays a key role in optimization, greatly enhancing the speed and model analysis capabilities of Frontline's Premium Solver Platform.