$MachinePrecision¶

Status: Stable

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

Description¶

$MachinePrecision

gives the number of decimal digits of precision used for machine-precision numbers.

Notes

Derived from the platform's DBL\_MANT\_DIG -- typically 53\*Log\[10,2\] (~ 15.9546) on IEEE 754 systems.

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)¶

Decimal digits carried by a machine double, 53 log10 2

In[5]:= $MachinePrecision
Out[5]= 15.9546

Implementation notes¶

A Protected OwnValue registered in system_constants_init (src/core.c) as expr_new_real(NUMERIC_MACHINE_PRECISION_DIGITS) — the number of decimal digits in a machine double (~15.95).

Attributes: Protected.

References¶

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

Notes & additional examples¶

Notes¶

$MachinePrecision is a read-only Protected OwnValue giving the number of decimal digits in a machine double, 53 · log₁₀ 2 ≈ 15.9546. It is the precision N[expr] (with no second argument) works at, and the threshold that separates machine-precision reals from the arbitrary-precision MPFR path.

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