C++ float storage

Question

Possible Duplicate:
Dealing with accuracy problems in floating-point numbers

Code:

float flt = 78983636;  // stores 78983632. as seen in debugger
flt = 79282056;        // stores 79282056.

Why is it not able to accurately store 1st value, but able to for the 2nd value which is larger?

"Larger" has little to do with this. Please see the answer I gave to another question (it's about Java and doubles, but the same concepts apply): http://stackoverflow.com/questions/7811112/why-is-long9223372036854665200d-giving-me-9223372036854665216/7811169#7811169 — NPE, Dec 14 '11 at 16:15
[What Every Computer Scientist Should Know About Floating-Point Arithmetic](http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html) — Joe, Dec 14 '11 at 16:18
Or to make a simple example: Assume you can only store a `n` as integer and it represents `10^n`. Now you can perfectly store 1000, 10.000 and so on but will have a hard time representing even 5 correctly. Similar principle for floats - it just gets a bit more complicated since we want to store more than just 2^something . — Voo, Dec 14 '11 at 18:05

score 6 · Accepted Answer · answered Dec 14 '11 at 16:20

A typical 32-bit float has about 24 bits of integer precision. That you're able to store your value precisely even though it's larger is simply because it hits a sweet spot that looks proper as an integer, while the other one does not.

Specifically the number 79282056 is stored as 1.1813947 * 2²⁶, or 79282056.2526208. So it's not exact, there's some digits after the decimal point that you omitted.

You can use this converter to inspect the mantissa, sign and exponent used to store any floating-point number.

C++ float storage

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