4 ms·

I'm not an expert on the ins-and-outs of floating-point numbers, but I've always heard fp types have a disproportionately large amount of their accuracy at valu

I'm not an expert on the ins-and-outs of floating-point numbers, but I've always heard fp types have a disproportionately large amount of their accuracy at values < 1. My guess is that it's not that wasteful sticking with floats or doubles. What I do wish the languages I used had support for, is number types that the user could clamp to a specific range. It would be nice to have my code throw an error if some function resulted in clipped audio, for example. I mean, without the programmer writing any extra code, of course.

sgtnoodle 6y ago
You're likely thinking of subnormal or denormal numbers, which helps floating point representation better represent tiny numbers near zero. The typical floating point number is normalized so that it's 1.xxxx*base^exponent. Since the 1 is always there, it is made implicit as a rule and only xxxx and exponent is stored in memory. There's a limit to the range of the exponent, though, and so for very tiny numbers near zero, the exponent is capped at its smallest value and the rule changes to have an implicit 0 instead of 1. Then, you can get a few more orders of magnitude 0xxx, 00xx, 000x, etc. You gradually trade significant digits for more negative exponents. I don't think it really helps for the interval 0 to 1, but rather for the interval 0 to 0.000000000000000000000000000000000001 or whatever. It doesn't give you more significant digits, but rather a gradual degradation of significant digits as they get used for exponents. Subnormal numbers are a bit controversial because of their relative utility vs. added complexity to implement them, especially in hardware.