MATLAB: Single versus double precision, what’s going on here

doubleprecisionsingle

Why does: >> 14+18300+200000+5000000+550000000

ans =

555218314

But: >> single(14)+single(18300)+single(200000)+single(5000000)+single(550000000)

ans =

555218304

Am I missing something? Thanks!

Best Answer

Hint--(a very large one :) )

 single(550000000)+single(5000000)+single(200000)+single(18300)
ans = ???

Related Solutions

MATLAB: Single precision and Double Precision (Looking for explanation why are they different in the “gap” of precision number)

>> eps(0.3)
ans =
      5.55111512312578e-17
>> eps(single(0.3))
ans =
  single
    2.980232e-08
>> eps(1)
ans =
      2.22044604925031e-16
>> eps(single(1))
ans =
  single
    1.192093e-07

So, Yes, there are differences.

IEEE 754 Single Precision is the number format used for storing single precision. It has a mantissa of 23 stored bits, so in the range of 1.0, numbers are 2^(-23) part.

IEEE 754 Double Precision is the number format used for storing double precision. It has a mantissa of 52 stored bits, so in the range of 1.0, numbers are 2^(-52) apart

MATLAB: Conversion to single is out of range

The keyword here is normalized.

Note that the realmin documentation clearly states "Smallest normalized floating-point number" (I added the bold), so what realmin returns is not the smallest possible single value... it is the smallest possible normalized single value... and clearly there are a few subnormal (or denormal) values that are smaller than that!

There are plently of resources on the web that will explain subnormal floating point numbers much better than I can, you might as well start here: https://en.wikipedia.org/wiki/Denormal_number

https://blogs.mathworks.com/cleve/2014/07/21/floating-point-denormals-insignificant-but-controversial-2/

"single() of a small number outside of the valid range returns an invalid value."

No, that value is a perfectly valid subnormal single floating point number.

"MATLAB apparently produces values that are out of range for IEEE 754, 32-bit single precision"

In fact MATLAB correctly interpreted IEEE 754-2008, which allows for subnormal values. Apparently by default many C compilers do NOT handle denormal floating point numbers according to IEEE 754.

Best Answer

Related Solutions

MATLAB: Single precision and Double Precision (Looking for explanation why are they different in the “gap” of precision number)

MATLAB: Conversion to single is out of range

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