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$MaxNumber

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

$MaxNumber
    gives the maximum arbitrary-precision number that can be
    represented on this computer system.

With USE_MPFR builds, this is the largest finite value at machine
precision under MPFR's current exponent range; otherwise it equals
$MaxMachineNumber.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= $MachinePrecision
Out[1]= 15.9546

In[2]:= $MachineEpsilon
Out[2]= 2.22045e-16

In[3]:= {$MinMachineNumber, $MaxMachineNumber}
Out[3]= {2.22507e-308, 1.79769e+308}

In[4]:= MachineNumberQ[$MaxNumber]   (* MPFR, not machine *)
Out[4]= False

Implementation notes

A Protected OwnValue registered in system_constants_init (src/core.c). In a USE_MPFR build it is the largest finite value at machine precision (DBL_MANT_DIG bits), computed by mpfr_set_inf then mpfr_nextbelow and stored via expr_new_mpfr_move; without MPFR it collapses to expr_new_real(DBL_MAX).

Attributes: Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References