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$MinNumber

Status: Stable

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

Description

$MinNumber

gives the minimum positive arbitrary-precision number that can be represented on this computer system.

Notes With USE\_MPFR builds, this is the smallest positive value at machine precision under MPFR's current exponent range; otherwise it equals $MinMachineNumber.

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[$MinNumber]
Out[5]= Real

Never larger than the machine minimum

In[6]:= $MinNumber <= $MinMachineNumber
Out[6]= True

Implementation notes

A Protected OwnValue registered in system_constants_init (src/core.c). Under USE_MPFR it is the smallest positive value at machine precision (mpfr_set_zero then mpfr_nextabove, stored via expr_new_mpfr_move); without MPFR it collapses to expr_new_real(DBL_MIN).

Attributes: Protected.

References

See also: $MachinePrecision, $MachineEpsilon, $MinMachineNumber, $MaxMachineNumber, $MaxNumber

Notes & additional examples

Notes

$MinNumber is a read-only Protected OwnValue: the smallest positive number Mathilda can represent. In a USE_MPFR build it is the smallest positive value at machine precision (mpfr_set_zero then mpfr_nextabove), far below $MinMachineNumber thanks to MPFR's exponent range. Without MPFR it collapses onto DBL_MIN, equal to $MinMachineNumber.

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