Built-in Mathematica Symbol

MachinePrecision

MachinePrecision
is a symbol used to indicate machine-number precision.

MORE INFORMATION

The numerical value of MachinePrecision is $MachinePrecision.

Precision[1.] gives MachinePrecision.

MachinePrecision is the default specification for precision in N and other numerical functions.

Approximate real numbers are assumed to have precision specified by MachinePrecision if fewer than $MachinePrecision explicit digits are entered.

The option setting WorkingPrecision->MachinePrecision specifies that internal computations in numerical functions should be done with machine numbers.

MachinePrecision is treated as a numeric constant, with attribute Constant.

EXAMPLES

CLOSE ALL

Basic Examples (2)

MachinePrecision is treated as an exact numeric quantity:

Use like any number:

The number of bits represented:

MachinePrecision is treated as an exact numeric quantity:

Use like any number:

The number of bits represented:

In[4]:=

Out[4]=

Scope (2)

The machine number approximating

:

An arbitrary-precision number approximating

to the same precision as machine numbers:

Use machine-number arithmetic to solve a differential equation:

Use double machine precision:

Compare the two solutions:

Applications (3)

Evaluate to double machine precision:

Use machine precision for the default precision argument in a function definition:

Make sure computations are carried out with the same precision as machine numbers:

Without fixing the precision, the resulting precision may be lower:

Properties & Relations (4)

Numbers with just a few digits entered are assumed to have machine precision:

Precision is based on the number of digits when more than $MachinePrecision + 1 are entered:

MachinePrecision is a numerical constant while $MachinePrecision evaluates to a number:

MachinePrecision is numerically Equal to $MachinePrecision:

$MachinePrecision is the machine-precision approximation to MachinePrecision:

MachinePrecision times the number of bits per digit gives the binary machine precision:

Digits beyond the known precision are represented as Indeterminate: