WOLFRAM

Wolfram Language & System Documentation Center
Wolfram Language Home Page »

SetAccuracy
✖
SetAccuracy

✖
SetAccuracy[expr,a]

yields a version of expr in which all numbers have been set to have accuracy a.

Details

  • When SetAccuracy is used to increase the accuracy of a number, the number is padded with zeros. The zeros are taken to be in base 2. In base 10, the additional digits are usually not zeros.
  • SetAccuracy returns an arbitrary‐precision number even if the number of significant digits obtained will be less than $MachinePrecision.
  • When expr contains machine‐precision numbers, SetAccuracy[expr,a] can give results that differ from one computer system to another.
  • SetAccuracy will first expose any hidden extra digits in the internal binary representation of a number, and, only after these are exhausted, add trailing zeros. »
  • 0.004``25 generates a number with all trailing digits zero and accuracy 25 on any computer system.
  • SetAccuracy[expr,a] does not modify expr itself.

Examples

open allclose all

Basic Examples  (2)Summary of the most common use cases

Set the accuracy of all numbers in an expression to 20:

In[1]:=1
✖
https://wolfram.com/xid/0enwibmvm-igltr4
Out[1]=1

Convert from a machine number to an arbitrary-precision number with accuracy 32:

In[1]:=1
✖
https://wolfram.com/xid/0enwibmvm-fxpsa6
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0enwibmvm-geborj
Out[2]=2

Scope  (5)Survey of the scope of standard use cases

Set the accuracy of a complex number:

In[1]:=1
✖
https://wolfram.com/xid/0enwibmvm-kiqka
Out[1]=1

Convert approximate numbers to exact rational numbers:

In[1]:=1
✖
https://wolfram.com/xid/0enwibmvm-cua60p
Out[1]=1

The result has trailing zeros once any hidden digits are exposed:

In[1]:=1
✖
https://wolfram.com/xid/0enwibmvm-vzjus

SetAccuracy does not affect exact powers:

In[1]:=1
✖
https://wolfram.com/xid/0enwibmvm-cgmhdi
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0enwibmvm-dnui4j
Out[2]=2

This allows you to, for example, change the accuracy of polynomial coefficients:

In[3]:=3
✖
https://wolfram.com/xid/0enwibmvm-dnzlyq
In[4]:=4
✖
https://wolfram.com/xid/0enwibmvm-bmjnp
Out[4]=4

Inexact powers are modified:

In[5]:=5
✖
https://wolfram.com/xid/0enwibmvm-qn4emm
Out[5]=5

Special rules may apply to data objects:

In[1]:=1
✖
https://wolfram.com/xid/0enwibmvm-dzy2xd
Out[1]=1

For an InterpolatingFunction object, SetAccuracy changes the appropriate data only:

In[2]:=2
✖
https://wolfram.com/xid/0enwibmvm-czn2jw
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0enwibmvm-g7kuk2

It works as an approximate function, but with arithmetic appropriate for the modified data:

In[4]:=4
✖
https://wolfram.com/xid/0enwibmvm-b58wqk
Out[4]=4

Applications  (1)Sample problems that can be solved with this function

Find the roundoff error in evaluating an expression with machine numbers:

In[1]:=1
✖
https://wolfram.com/xid/0enwibmvm-c56v6m
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0enwibmvm-8rl9e
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0enwibmvm-bn5rtu
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0enwibmvm-comktm
Out[4]=4

This dominates the approximation error since the increment is so small:

In[5]:=5
✖
https://wolfram.com/xid/0enwibmvm-bfvmf8
Out[5]=5

Properties & Relations  (2)Properties of the function, and connections to other functions

SetAccuracy just sets the precision of numbers, while N works adaptively:

In[1]:=1
✖
https://wolfram.com/xid/0enwibmvm-cxhcqf
Out[1]=1

Since N works adaptively, the result has the requested accuracy of 20:

In[2]:=2
✖
https://wolfram.com/xid/0enwibmvm-bst5qf
Out[2]=2

Use SetAccuracy:

In[3]:=3
✖
https://wolfram.com/xid/0enwibmvm-buajcq
Out[3]=3

The accuracy is less than 20 because of the way the exponential function magnifies the result:

In[4]:=4
✖
https://wolfram.com/xid/0enwibmvm-hubzyl
Out[4]=4

SetAccuracy effectively evaluates Exp with argument 10 to accuracy 20:

In[5]:=5
✖
https://wolfram.com/xid/0enwibmvm-bjrxnz
Out[5]=5

For nonzero numbers , SetAccuracy[x,a] is equivalent to SetPrecision[x,a+e]:

In[1]:=1
✖
https://wolfram.com/xid/0enwibmvm-rk3de
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0enwibmvm-igbinz
Out[2]=2

e is given by RealExponent:

In[3]:=3
✖
https://wolfram.com/xid/0enwibmvm-t3vjn
Out[3]=3
Wolfram Research (1991), SetAccuracy, Wolfram Language function, https://reference.wolfram.com/language/ref/SetAccuracy.html.
✖
Wolfram Research (1991), SetAccuracy, Wolfram Language function, https://reference.wolfram.com/language/ref/SetAccuracy.html.

Text

Wolfram Research (1991), SetAccuracy, Wolfram Language function, https://reference.wolfram.com/language/ref/SetAccuracy.html.

✖
Wolfram Research (1991), SetAccuracy, Wolfram Language function, https://reference.wolfram.com/language/ref/SetAccuracy.html.

CMS

Wolfram Language. 1991. "SetAccuracy." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SetAccuracy.html.

✖
Wolfram Language. 1991. "SetAccuracy." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SetAccuracy.html.

APA

Wolfram Language. (1991). SetAccuracy. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SetAccuracy.html

✖
Wolfram Language. (1991). SetAccuracy. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SetAccuracy.html

BibTeX

@misc{reference.wolfram_2025_setaccuracy, author="Wolfram Research", title="{SetAccuracy}", year="1991", howpublished="\url{https://reference.wolfram.com/language/ref/SetAccuracy.html}", note=[Accessed: 29-March-2025 ]}

✖
@misc{reference.wolfram_2025_setaccuracy, author="Wolfram Research", title="{SetAccuracy}", year="1991", howpublished="\url{https://reference.wolfram.com/language/ref/SetAccuracy.html}", note=[Accessed: 29-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_setaccuracy, organization={Wolfram Research}, title={SetAccuracy}, year={1991}, url={https://reference.wolfram.com/language/ref/SetAccuracy.html}, note=[Accessed: 29-March-2025 ]}

✖
@online{reference.wolfram_2025_setaccuracy, organization={Wolfram Research}, title={SetAccuracy}, year={1991}, url={https://reference.wolfram.com/language/ref/SetAccuracy.html}, note=[Accessed: 29-March-2025 ]}