# \$MinPrecision

gives the minimum number of digits of precision to be allowed in arbitraryprecision numbers.

# Details

• The default value of \$MinPrecision is 0.
• Positive values of \$MinPrecision make the Wolfram Language pad arbitraryprecision numbers with zero digits to achieve the specified nominal precision. The zero digits are taken to be in base 2, and may not correspond to zeros in base 10.
• \$MaxPrecision=\$MinPrecision=n makes the Wolfram Language do fixedprecision arithmetic.
• \$MinPrecision is measured in decimal digits, and need not be an integer.

# Examples

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## Basic Examples(2)

Make sure precision is kept at or above machine precision in a calculation:

Do a computation with fixed 20-digit precision:

## Applications(1)

Power method for the largest eigenvalue using fixed precision:

Find the largest eigenvalue of the 4×4 Hilbert matrix to 47 digits:

Without fixed precision the result indicates lost precision:

The fixed precision is correct to 47 digits since the iteration is self-correcting:

## Possible Issues(1)

\$MinPrecision does not affect parts of computations with machine numbers:

If needed, use SetPrecision to eliminate machine numbers from the input:

Wolfram Research (1996), \$MinPrecision, Wolfram Language function, https://reference.wolfram.com/language/ref/\$MinPrecision.html (updated 2003).

#### Text

Wolfram Research (1996), \$MinPrecision, Wolfram Language function, https://reference.wolfram.com/language/ref/\$MinPrecision.html (updated 2003).

#### CMS

Wolfram Language. 1996. "\$MinPrecision." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2003. https://reference.wolfram.com/language/ref/\$MinPrecision.html.

#### APA

Wolfram Language. (1996). \$MinPrecision. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/\$MinPrecision.html

#### BibTeX

@misc{reference.wolfram_2022_\$minprecision, author="Wolfram Research", title="{\$MinPrecision}", year="2003", howpublished="\url{https://reference.wolfram.com/language/ref/\$MinPrecision.html}", note=[Accessed: 09-December-2022 ]}

#### BibLaTeX

@online{reference.wolfram_2022_\$minprecision, organization={Wolfram Research}, title={\$MinPrecision}, year={2003}, url={https://reference.wolfram.com/language/ref/\$MinPrecision.html}, note=[Accessed: 09-December-2022 ]}