$MinMachineNumber¶

Status: Stable

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

Description¶

$MinMachineNumber

gives the smallest positive machine-precision number that can be represented in normalized form on this computer system.

Notes

Equals the platform's DBL\_MIN.

Examples (5)¶

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 (1)¶

The smallest positive normalised double, DBL_MIN

In[5]:= $MinMachineNumber
Out[5]= 2.22507e-308

Implementation notes¶

A Protected OwnValue set in system_constants_init (src/core.c) to expr_new_real(DBL_MIN), the smallest positive normalized IEEE 754 double.

Attributes: Protected.

References¶

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

Notes & additional examples¶

Notes¶

$MinMachineNumber is a read-only Protected OwnValue equal to <float.h> DBL_MIN, the smallest positive normalised machine double (≈ 2.22507×10⁻³⁰⁸). A positive machine-precision result below it underflows; the arbitrary-precision floor $MinNumber is smaller.

The value is a fixed machine constant on every IEEE 754 platform.