$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.

Notes

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

Examples (6)¶

Every input below was run against the current Mathilda build and its output recorded.

Basic examples (4)¶

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}

MPFR, not machine

In[4]:= MachineNumberQ[$MaxNumber]
Out[4]= False

Applications (2)¶

A Real; its literal value is build-dependent

In[5]:= Head[$MaxNumber]
Out[5]= Real

Never smaller than the machine maximum

In[6]:= $MaxNumber >= $MaxMachineNumber
Out[6]= True

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.

References¶

Source: src/core.c
Specification: docs/spec/builtins/expression-information.md

Notes & additional examples¶

Notes¶

$MaxNumber is a read-only Protected OwnValue: the largest finite number Mathilda can represent. In a USE_MPFR build it is the largest finite value at machine precision (DBL_MANT_DIG bits) with MPFR's enormous exponent range — computed by mpfr_set_inf then mpfr_nextbelow — so it is astronomically larger than $MaxMachineNumber. Without MPFR there is no arbitrary-precision representation and it collapses onto DBL_MAX, equal to $MaxMachineNumber.

Because the literal value therefore depends on whether MPFR was linked, the examples above are structural; $MaxNumber >= $MaxMachineNumber holds in either build.