There are plenty of libraries which makes dealing with fixed-point relatively easy.
I think GP is alluding to issues you get when you have a mix of scales. Like floating-point, fixed-point will have a limited precision range around the origin. In contrast to floating-point, the range for fixed-point is smaller but evenly spaced.
Say you have 32:32 fixed-point. You can then represent numbers in multiple of ~0.2e-9. So if you need to calculate distances in nanometers, perhaps due to a short timestep in a simulation, you have hardly any precision to work with.
The obvious way around this is to pull out a scale factor, say 1e-9 since you know you'll be in the nano-range. Now the numbers you're working with are back on the order of 1 with lots of precision, however you need to apply the scale factor when you actually want to use the number, and now you have to be careful not to overflow when multiplying two or more scaled numbers. This is part of the programmer overhead GP alluded to.
> The obvious way around this is to pull out a scale factor, say 1e-9 since you know you'll be in the nano-range. Now the numbers you're working with are back on the order of 1 with lots of precision, however you need to apply the scale factor when you actually want to use the number, and now you have to be careful not to overflow when multiplying two or more scaled numbers.
Do that rescaling automatically and have a system that just keeps track of the scale and you've just implemented floats. (:
I think GP is alluding to issues you get when you have a mix of scales. Like floating-point, fixed-point will have a limited precision range around the origin. In contrast to floating-point, the range for fixed-point is smaller but evenly spaced.
Say you have 32:32 fixed-point. You can then represent numbers in multiple of ~0.2e-9. So if you need to calculate distances in nanometers, perhaps due to a short timestep in a simulation, you have hardly any precision to work with.
The obvious way around this is to pull out a scale factor, say 1e-9 since you know you'll be in the nano-range. Now the numbers you're working with are back on the order of 1 with lots of precision, however you need to apply the scale factor when you actually want to use the number, and now you have to be careful not to overflow when multiplying two or more scaled numbers. This is part of the programmer overhead GP alluded to.