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$MinPrecision
gives the minimum number of digits of precision to be allowed in arbitrary‐precision numbers.
Details
- The default value of $MinPrecision is 0.
- Positive values of $MinPrecision make the Wolfram Language pad arbitrary‐precision 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 fixed‐precision arithmetic.
- $MinPrecision is measured in decimal digits, and need not be an integer.
Examples
open allclose allBasic Examples (2)Summary of the most common use cases
Make sure precision is kept at or above machine precision in a calculation:
https://wolfram.com/xid/01z0ic1ps66-bn556
Do a computation with fixed 20-digit precision:
https://wolfram.com/xid/01z0ic1ps66-k6jd0i
Applications (1)Sample problems that can be solved with this function
Power method for the largest eigenvalue using fixed precision:
https://wolfram.com/xid/01z0ic1ps66-bzrfhq
Find the largest eigenvalue of the 4×4 Hilbert matrix to 47 digits:
https://wolfram.com/xid/01z0ic1ps66-evvn9
Without fixed precision the result indicates lost precision:
https://wolfram.com/xid/01z0ic1ps66-i24flk
The fixed precision is correct to 47 digits since the iteration is self-correcting:
https://wolfram.com/xid/01z0ic1ps66-bzso9p
Possible Issues (1)Common pitfalls and unexpected behavior
$MinPrecision does not affect parts of computations with machine numbers:
https://wolfram.com/xid/01z0ic1ps66-hvro2d
https://wolfram.com/xid/01z0ic1ps66-bvwbxv
If needed, use SetPrecision to eliminate machine numbers from the input:
https://wolfram.com/xid/01z0ic1ps66-imodnp
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).
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.
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
Wolfram Language. (1996). $MinPrecision. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/$MinPrecision.html
BibTeX
@misc{reference.wolfram_2024_$minprecision, author="Wolfram Research", title="{$MinPrecision}", year="2003", howpublished="\url{https://reference.wolfram.com/language/ref/$MinPrecision.html}", note=[Accessed: 20-January-2025
]}
BibLaTeX
@online{reference.wolfram_2024_$minprecision, organization={Wolfram Research}, title={$MinPrecision}, year={2003}, url={https://reference.wolfram.com/language/ref/$MinPrecision.html}, note=[Accessed: 20-January-2025
]}