Matlab returns Inf for 10^1000.

Why is 10^1000 unrepresentable in Matlab?

Answer 1

[Walter Roberson]

MATLAB uses IEEE 754 Double Precision Floating Point. The maximum representable value is approximately 1E+308

The File Exchange has an extended precision integer tool.

The Symbolic Toolbox represents values with potentially longer precision. I am not certain what the limit is; 10^10000 possibly, maybe higher.

[David]

Is there a formula for calculating the largest storable value by a n bit long string? Like, for single it's 2^31 - 1. Or, have I been misinformed?

[Roger Stafford]

In IEEE 754 double precision floating point numbers the largest possible finite number representable is 2^1024*(1-2*(-53)) and is called 'realmax'. The total bit string which represents these numbers is 64 bits long with one bit for the sign, 11 bits for the exponent, and 53 bits, one of which is implicit ("hidden"), for the significand (mantissa).

(Corrected)

Answer 2

[John D'Errico]

As Per and Roger have explained, the issue is that a double only goes so far. Floating point numbers use a fixed number of bits to encode any number within reasonable limits. However, some numbers are just too big. For them, you need a tool in matlab that is designed to handle them. Thus

sym('10^1000')
ans =
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

My HPF can do it too.

hpf('1e1000',100)
ans =
1.e1000

As well as my vpi tool, or the enhanced version of that tool, vpij.

vpi(10)^1000
ans =
    10000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000

So MATLAB CAN represent that number, but only if you use the proper data type.

Answer 3

[per isakson]

Because

    >> realmax( 'double' ) 
    ans =
      1.7977e+308

See Floating-Point Numbers