Why is the maximum number of elements in an array or matrix in 64-Bit MATLAB limited to 2^48-1 and not 2^63-1 ?

The largest valid index into an array for the 32-bit MATLAB is 2^31-1.

Similarly, I expect the largest valid index for the 64-bit MATLAB is 2^63-1.

I want to know what is the significant of the number 2^48-1 in limiting the array/matrix elements.

Answer 1

[MathWorks Support Team]

The current 64-bit processors from AMD and Intel do not actually support 64-bit addressing. They only have 40 physical address pins and can support 48-bits virtual addressing. (For more information, please see https://en.wikipedia.org/wiki/X86-64#Architectural_features.)

Please note that the theoretical limit of 2^48-1 elements cannot currently be reached due to other limitations such as available system memory (This would require about ~300TB for 8-bit data) and the process space limit of the operating system, which on 64-bit Windows is just 8TB (or 2^43). For more information please refer 

https://mskb.pkisolutions.com/kb/294418

[Walter Roberson]

The largest publicly known unified-memory systems in the world are (as of early 2021), Linux systems from HP that can access 160 Terabytes; these need the full 48 bits of address space.

https://www.hpe.com/us/en/newsroom/press-release/2017/05/a-new-computer-built-for-the-big-data-era.html