How do I calculate the min/max decimal numbers that could be represented in binary 16, 32, 64 IEEE 754 floating point?
0
votes
In a particular programming language? Or in general?
- alias
In general, I'm just writing a simple algorithm in pseudo-code that is to allow a user to enter a fixed point number (positive or negative) and based on the number entered, determine if the number can be represented in binary16, 32 or 64 floating point representation.
- Mike Brathwaite
Remember that just because a fixed-point value is within a range, it doesn't mean it can be represented. FP values "skip around" at any range.
- alias
@LeventErkok: And, if they are allowing rounding during conversion, the greatest input number that converts to a finite value is different from the greatest representable value.
- Eric Postpischil
@EricPostpischil Quite right, rounding mode adds another layer of complexity.
- alias
1 Answers
1
votes
The NORMAL ranges are:
- 16-bit (half precision): ±6.10e-5 to ±65504.0
- 32-bit (single precision): ±1.18e−38 to ±3.4e38
- 64-bit (double precision): ±2.23e−308 to ±1.80e308
If you allow for DENORMALS as well, then minumum values are:
- 16-bit: ±5.96e-8
- 32-bit: ±1e-45
- 64-bit: ±5e-324
Always keep in mind that just because a number is in this range doesn't mean it can be exactly represented. At any range, floating-point numbers necessarily skip values due to cardinality reasons. The classic example is 1/3 which has no exact representation in any finite precision. In general you can only precisely represent those numbers that are called "dyadic," i.e., those of the form A/2^B for some A and B; provided the result falls into the dynamic range.
