How to convert packed integer (16.16) fixed-point to float?

Question

How to convert a "32-bit signed fixed-point number (16.16)" to a float?

Is (fixed >> 16) + (fixed & 0xffff) / 65536.0 ok? What about -2.5? And -0.5?

Or is fixed / 65536.0 the right way?

(PS: How does signed fixed-point "-0.5" looks like in memory anyway?)

Answer 1

I assume two's complement 32 bit integers and operators working as in C#.

How to do the conversion?

fixed / 65536.0

is correct and easy to understand.

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(fixed >> 16) + (fixed & 0xffff) / 65536.0

Is equivalent to the above for positive integers, but slower, and harder to read. You're basically using the distributive law to separate a single division into two divisions, and write the first one using a bitshift.

For negative integers fixed & 0xffff doesn't give you the fractional bits, so it's not correct for negative numbers.

Look at the raw integer -1 which should map to -1/65536. This code returns 65535/65536 instead.

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Depending on your compiler it might be faster to do:

fixed * (1/65536.0)

But I assume most modern compilers already do that optimization.

How does signed fixed-point "-0.5" looks like in memory anyway?

Inverting the conversion gives us:

RoundToInt(float*65536)

Setting float=-0.5 gives us: -32768.