SEARCH MATHEMATICA 8 DOCUMENTATION

THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.

Built-in Mathematica Symbol

$MinMachineNumber

$MinMachineNumber
is the smallest positive machine-precision number that can be used on a particular computer system.

The smallest hardware floating-point number:

Numbers smaller than $MinMachineNumber are represented as arbitrary-precision numbers:

Find the minimum machine number algorithmatically:

$MinMachineNumber has the smallest possible binary exponent and all but one bits set to 0:

$MaxMachineNumber×$MinMachineNumber is 4.×(1.-$MachineEpsilon/2):

Accuracy[0.] is -Log[10, $MinMachineNumber]:

Mathematica uses arbitrary-precision to represent numbers that would be denormalized:

This conversion can be prevented in Compile and some other functions with a system option:

The smallest denormalized machine number:

Restore the option to its default: