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IntegerLength

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

IntegerLength[n] gives the number of decimal digits in the integer n.
IntegerLength[n, b] gives the number of base b digits in n.
IntegerLength ignores the sign of n; IntegerLength[0] is 0.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= IntegerLength[123456789]
Out[1]= 9

In[2]:= IntegerLength[100!, 2]
Out[2]= 525

In[3]:= Table[IntegerLength[100!, n], {n, 2, 20}]
Out[3]= {525, 332, 263, 227, 204, 187, 175, 166, 158, 152, 147, 142, 138, 135, 132, 129, 126, 124, 122}

In[1]:= IntegerLength[]
Out[1]= IntegerLength[]

In[2]:= IntegerLength[1, 2, 3, 4]
Out[2]= IntegerLength[1, 2, 3, 4]

In[1]:= IntegerLength[1.1234]
Out[1]= IntegerLength[1.1234]

Implementation notes

builtin_integerlength returns the number of base-b digits of |n| (default base 10). For bases <= 62 it uses GMP's mpz_sizeinbase, which is exact for power-of-two bases and at most one too large otherwise — corrected by comparing |n| against base^(s-1) (intlen_count_digits). For arbitrary-precision bases it counts via repeated mpz_tdiv_q. IntegerLength[0] is 0. Validates arity (IntegerLength::argt), numeric non-integer n (::int), and base >= 2 (::ibase); symbolic n returns NULL.

  • Protected, Listable. Threads element-wise over a list of integers in

Attributes: Listable, Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References

Notes & additional examples

Worked examples

In[1]:= IntegerLength[12345]
Out[1]= 5

In[1]:= IntegerLength[2^1000]
Out[1]= 302

In[1]:= IntegerLength[2^1000, 2]
Out[1]= 1001

In[2]:= IntegerLength[100!]
Out[2]= 158

Notes

IntegerLength[n] returns the number of decimal digits of n, and IntegerLength[n, b] the number of base-b digits. Working at arbitrary precision, it answers questions that overflow fixed-width arithmetic: 2^1000 has 302 decimal digits but exactly 1001 binary digits, and 100! is a 158-digit number. The sign of n is ignored and IntegerLength[0] is 0.