The title says it all: I want to calculate an exponent in matlab with big numbers, but I get overflow and it just returns infinity.
>> 100^1000
ans =
As Daniel has already pointed out, it's too big a number to be even outputted by MATLAB itself. This number is obtained with realmax for different datatypes. As an alternative to represent/use such huge numbers, you can use the corresponding mantissa
and exponent
with base-10 representation
instead, which is the usual MATLAB representation. The function to get those two is listed here -
function [mantissa, base10_exponent] = base10_mantissa_exponent(base,exponent)
act_exp = exponent*log10(abs(base));
base10_exponent = floor(act_exp);
mantissa = power(10,act_exp - base10_exponent);
if rem(exponent,2)==1 && sign(base)==-1
mantissa = -mantissa;
end
return;
Few example runs and comparisons with actual MATLAB runs for validation are listed next.
Ex #1
base = -125.343;
exponent = 101;
usual_approach = base^exponent
[mantissa, base10_exponent] = base10_mantissa_exponent(base,exponent)
Output -
usual_approach =
-8.0930e+211
mantissa =
-8.0930
base10_exponent =
211
Ex #2 (problem discussed in the question)
base = 100;
exponent = 1000;
Output -
usual_approach =
Inf
mantissa =
1
base10_exponent =
2000
Working with 64bit floating point arithmetic, 100^1000
is inf
because it is larger than the largest possible value. If the symbolic math toolbox is available, use vpa
or sym
to work with large numbers:
sym('100^1000')
or
vpa('100^1000')
To deal with large numbers there is also the class High Precision Float, with which the result can be achieved by writing
a = hpf(100);
b = hpf(1000);
c = a^b;
which gives c = 1.e2000
. A call to struct(c)
provides informations on how the number is internally stored.
struct(c)
ans =
NumberOfDigits: [64 4]
DecimalBase: 4
Base: 10000
Numeric: 0
Sign: 1
Exponent: 2001
Migits: [1000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]