使C＃算法更有效

Question

I have a C# method that projects the value of a number from an interval to a target interval.
For example: we have an interval of -1000 and 9000 and a value of 5000; if we want to project this value to an interval of 0..100 we get 60.

Here is the method:

/// <summary>  
/// Projects a value to an interval
/// </summary>
/// <param name="val">The value that needs to be projected</param>  
/// <param name="min">The minimum of the interval the value comes from</param>  
/// <param name="max">The maximum of the interval the value comes from</param>  
/// <param name="intervalTop">The minimum of the interval the value will 
/// be projected to</param>  
/// <param name="intervalBottom">The maximum of the interval the value will 
/// be projected to</param>  
/// <returns>Projected value</returns> 
public decimal ProjectValueToInterval(decimal val,  
                                      decimal min,  
                                      decimal max,  
                                      decimal intervalBottom, 
                                      decimal intervalTop)  
{  
    decimal newMin = Math.Min(0, min);
    decimal valueIntervalSize = Math.Abs(max - newMin);
    decimal targetIntervalSize = Math.Abs(intervalTop - intervalBottom);

    decimal projectionUnit = targetIntervalSize / valueIntervalSize;

    return (val * projectionUnit) + Math.Abs((newMin * projectionUnit));
}

This method needs to be called for thousands of values.
I was wondering if there is a more efficient way to do this in C#? If yes, what changes do you suggest?

Answer 1

Only thousands of values? Do you really need to optimise this further? I can't imagine it's actually a bottleneck at the moment. Have you profiled the app to check that this is really an issue?

Given that the method is O(1), you're not going to make the most drastic kind of optimisation you normally aim at - improving the complexity.

Having said that - when you call this thousands of times, do any of the values stay constant? For example, are you using the same min and max repeatedly? If so, you could create a class which takes those values in the constructors and precomputes what it can, then has a method taking the rest of the parameters. This will improve things slightly, but I go back to my original point - only worry about this if it's actually causing problems.

Answer 2

The answers is: Do NOT use decimal for fast operations.

Is there any reason why float or double does not work for you?

Answer 3

Just maths. What you're "projecting" is a normalisation of ranges AB and A'-B' such that:

ratio r = (xA) / (BA) = (y-A') / (B'-A')

which using your terms is:

(val-min) / (max-min) = (returnValue-intervalBottom) / (intervalTop-intervalBottom)

which solves for returnValue as:

returnValue =  ((intervalTop-intervalBottom) * (val-min) / (max-min)) + intervalBottom

Answer 4

In addition to not using Decimal as has already been suggested, you could santise your max/min values somewhere else, so that you didn't need all those Abs calls all over the place.

I suspect that only part of this you need to do repeatedly is a floating point multiply followed (or proceeded) by a floating point add. Everything else can be pre-checked & pre-calculated.

Answer 5

You code appears more complex than it really needs to be. The formula is:

intervalTop + (intervalBottom - intervalTop) * (val - min) / (max - min);

which is much simpler than your version (and works for integral types). There's no conditional branches in there (the Math.Min call) or method calls. OK, it assumes that intervalTop < intervalBottom and min < max. If intervalTop, intervalBottom, min and max are constant for a set of values then you can precompute (intervalBottom - intervalTop) and (max - min) and use those results for all calls to the function. Another overhead you can eliminate is to inline the function into the calling loop. I don't know what C# (or rather the JIT compiler) does about inlining methods so this might already be happening under the hood.

If you can live with ints or float data types, one possible solution is to use SIMD but this would mean writing native assembler code which might break your requirements.