[Convert from Double to Single]

Hello Everyone,

Currently, during Simulation I have a issue, Please help me........

Issue : ( at the command windown)

value = 214748364.7 // Data type is default double.

value_single = single(value) // The result of this convertion is 214748368

my expectation value is value_single = 214748364.7

What is happened ?

Please help me.............!!!

Thank you in advance.

[Shubham Gupta]

I think What you are expecting is not possible for a single type value. It has something to do with the precision for single. Either reduce the value or if you want to use big numbers then I would suggest using double type.

[Binh Huynh Thanh]

Thank you Shubham,

Actually , the double type is good solution because it is 8 bytes and single is only 4 bytes. But this is a specical case, I would like to use the single data type. So, I had above issue.

Thank you.

Answer 1

[Walter Roberson]

>> flintmax('single')

ans =

  single

    16777216

your 214748368 exceeds that, so you have exceeded the point at which single precision floating point numbers start being spaced 1.0 or more further apart.

>> log2(214748364.7)
27.6780719044408

So you would need 28 bits at least just to represent the integer portion. https://en.wikipedia.org/wiki/Single-precision_floating-point_format says that for IEEE 754 single precision, there are only 23 explicit bits available for the fraction; there is also one "hidden" bit, so you can only get 24 bits worth but you need more than 28 bits for the representation.

>> eps(single(214748364.7))

ans =

  single

    16

[Binh Huynh Thanh]

Hello Walter Roberson,

Basically, I understood what you mean as below:

Sign bit: 1 bit

Exponent width: single

Significand precision: 24 bits (23 explicitly stored)

If the value have exceeded the threshold (2^24 = 16777216). The output value will be not exactly as expectation.

By the way, thank you very much.

[Steven Lord]

As a metaphor, unless he's talking to his accountants or the IRS Bill Gates probably doesn't describe his fortune down to the last cent. In casual conversation he rounds to a "nice" number. If you were to give him a $1 bill, it doesn't change how he reports his wealth. If you were to give him a million dollars, that might cause him to change his statement of his fortune (or that might require multiple millions.)

The "nice" number to which Gates rounds his wealth is the closest "representable" number to his actual wealth. How much money he would have to gain to change that nice number to the next larger or smaller representable number is eps, and if we operate on the assumption from the first paragraph it's somewhere between 1 and a million.

Since neither of us has as much money as Bill Gates does, our eps values are smaller ;)

[Binh Huynh Thanh]

@Steven Lord,

Your thinking is out of my mind