IntegerLength

The number of digits of $n$ in the given base — base 10 by default.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageIntegerLength✓↗

IntegerLength(n)the number of base-10 digits of $n$

IntegerLength(n, base)the number of digits in the given base

Typed signatures

Type	Package	Applies
(integer, integer?) -> integer	numerals	always

Domain: Numeral systems

Details

• The sign of $n$ is not counted — IntegerLength(-123) is 3, same as IntegerLength(123)
• IntegerLength(0) is 0, unlike IntegerDigits's one-element {0} — there is no shortest numeral for 0, only the empty one

Plot

Examples

Basic #

live ↗

In$\mathrm{IntegerLength}(12\,345)$Out$5$

Number of decimal digits

live ↗

In$\mathrm{IntegerLength}(123\,456\,789)$Out$9$

$100!$ takes 525 bits

live ↗

In$\mathrm{IntegerLength}(100!, 2)$Out$525$

Scope #

live ↗

In$\mathrm{IntegerLength}(2^{100})$Out$31$

$255 = \mathrm{ff}_{16}$

live ↗

In$\mathrm{IntegerLength}(255, 16)$Out$2$

Listable

live ↗

In$\mathrm{IntegerLength}(\bigl\lbrack1, 10, 100\bigr\rbrack)$Out$\bigl\lbrack1, 2, 3\bigr\rbrack$

Possible issues #

the sign is not counted

live ↗

In$\mathrm{IntegerLength}(-123)$Out$3$

0 has length 0, unlike its one-element IntegerDigits

live ↗

In$\mathrm{IntegerLength}(0)$Out$0$

About

Examples	8
Checked against	Wolfram Language 8 agreemathlib4 6 agree2 error
Crosswalk	Wolfram Language

Implementation

mappedmathlib4packages/oracle/src/mappings.ts

The length of Nat.digits, which is [] at 0, so 0 has length 0 as ours; natural n only.

mappedmathlib4packages/oracle/src/mappings.ts

As the one-argument row, in an integer base.

See also: IntegerDigits, IntegerReverse, IntegerString