| On the hardware, it's fundamentally integer arithmetic under the hood. Floating point itself is an implementation on top of that. With a slide rule it's basically truncated integers all the way, you're very limited on significant figures, you float the point in your head or some other way, and apply it afterward. You're constantly aware of any step where your significant figures drop below 3 because that's such a drastic drop from 3 down to 2. Or down to 1 which can really slap you in the face. The number of decimal places also is an integer naturally which is related to scientific notation. Whether a result is positite or negative is a simple flag. On a proper computer, integer addition, subtraction, and multiplication are exact. It's the division which produces integers which are not exact, since they can usually be truncated results, as they are written to memory at the bitness in use at the time, storing the whole-number portion of the quotient only. Integer arithmetic can usually be made as exact as you want and it helps to consciously minimize divisions, and if necessary offset/scale the operands beforehand such that the full range of quotients is never close enough to zero for the truncation to affect your immediate result within the number of significant figures necessary for your ultimate result to be completely reliable. The number of significant figures available on even an 8-bit computer just blows away the slide rule but not if you don't take full advantage of it. What sometimes happens is that zero-crossing functions, when the quotients are not offset, will fluctuate between naturally taking advantage of the enhanced bitness of the hardware for large values (blowing away the slide rule a huge amount of the time), while "periodically" dropping below the accuracy of a slide rule when some quotient, especially an intermediate one, is too near zero. Floating point or integer. If there's nobody keeping track of not just the magnitude of the possible values, but also the significant figures being carried at each point, your equations might not come out as good as a slide rule sometimes. Edit: IOW when the final reportable result is actually a floating point number where you need to have an accurate idea how many figures to the right of the decimal place are truly valid, it might be possible to use all integer calculations to your advantage from the beginning, and confidently place the decimal point as a final act. |