How to get 32 bit mathematical output?

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.

[Walter Roberson]

Are you using the Fixed Point Toolbox? That is the only toolbox that would have floating point output as small as 15 bit.

[vivek k]

i m computing cosd10=0.984807753012208 which is 15 bit,i want this into 32&64bit

[Randy Souza]

@vivek k: Please don't ask questions in all caps. It is the online equivalent of SHOUTING AT SOMEONE. Which is CONSIDERED RUDE! ;-)

[vivek k]

this is 1st time i m asking the question in in this forum, so not aware of caps lock. sorry for that

Answer 1

[Walter Roberson]

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.

[vivek k]

thank you for the ans, if i need some more digits say up to 32 digits or 64 digits, how to get it?

[Walter Roberson]

You could use the Symbolic Toolbox, or maybe the Fixed-point toolbox.

What would you do with 64 digits of accuracy of the cos of an angle? You know that is a much higher accuracy than we know the fundamental physical constants?? For example, Planck Distance, at which theories of the nature of Space-Time break down, below which space as we know it might not be continuous, is 1.616252E−35 meter, which is almost exactly 32 digits accuracy if you measure in millimeters. The Universe itself is estimated to be 4.35184307E26 meters in radius, so if you had cosd to 64 bits, you would be trying to locate something to about 100 times finer thank the Planck Distance relative to the entire Universe!

[vivek k]

thank you for responce. is it possible to get such value in matlab using symbolic toolbox?

[Walter Roberson]

I do not have the MuPAD symbolic toolbox to test with to be absolutely sure, but

vpa( cos(sym(10) * sym('pi') / sym(180)), 64 )

should produce the symbolic result (you will not be able to store the result in a double precision number, of course)

0.9848077530122080593667430245895230136706432517198424187900257524