MATLAB: How to get 32 bit mathematical output

32 bit floating bit o/p?

I am computing a series of equations and presently I'm getting a 15 bit floating point o/p, I need it in 32 bit and 64 bit.

Best Answer

0.984807753012208 is 15 digits, not 15 bits. You are also missing printing out some of the digits: use

sprintf('%.99g\n', TheVariable)

to see the full list of digits.

Each decimal digit corresponds to log2(10) bits, which is just under 3 1/3 bits per decimal digit. 15 decimal digits therefore corresponds to about 49 bits. But really it is 16 digits you are getting: the next in sequence happens to be 0 so it is omitted from the printout. 16 decimal digits corresponds to 53 bits of accuracy. The remaining bits in a 64 bit double precision word correspond to sign information and to the exponent (... x 2^(-1) in this particular case.)

So you are already getting full 64 bit accuracy.

Related Solutions

MATLAB: Where do all these digits come from

3.141592653589793115997963468544185161590576171875

is what is stored for pi -- just a little longer than you happened to display.

If you are using MATLAB on MS Windows, then the digits you see output after the 16th are either 0 or garbage that happens to be randomly in the buffer. For MATLAB on MS Windows, to see numbers accurately, you should use num2strexact from the File Exchange.

If you are using MATLAB on Linux, then historically after some point (I no longer recall the length), fprintf() would produce zeros instead of correct digits.

If you are using MATLAB on Mac, then it has always produced all of the correct digits.

The digits you see are the base 10 representation of the binary value that is stored.

>> num2hex(pi)
ans =
    '400921fb54442d18'
>> pi-hex2num('400921fb54442d17')
ans =
      4.44089209850063e-16
>> hex2num('400921fb54442d19')-pi
ans =
      4.44089209850063e-16

>> sym(hex2num('400921fb54442d18'),'d')
ans =
3.141592653589793115997963468544185161590576171875
>> sym(hex2num('400921fb54442d19'),'d')
ans =
3.141592653589793560087173318606801331043243408203125
>> vpa(sym(pi)) 
ans =
3.141592653589793238462643383279502884197169399375105820974944592307816406286209

Comparing, you can see that the '400921fb54442d18' version is a little too low, and the '400921fb54442d19' version is a little too high. The value that was used, '400921fb54442d18', was chosen as being closer to the infinitely precise version of pi than the next number '400921fb54442d19' is.

MATLAB: What is the concept behind symbolic toolbox

MATLAB uses hardware instructions to calculate most of the basic operations; those hardware instructions work on fixed-length binary numbers, such as hardware addition, hardware division, and so on.

The symbolic toolbox does not use fixed length binary numbers. The symbolic toolbox uses chains of blocks to represent numbers. Instead of using hardware instructions to do the basic operations, it calculates everything in software, using slower libraries that handle the chains of data.

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Related Solutions

MATLAB: Where do all these digits come from

MATLAB: What is the concept behind symbolic toolbox

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