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DigitCount

Status: Stable

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

Description

DigitCount[n] gives a list of the counts of digits 1, 2, ..., 9, 0 in the base-10 representation of n.
DigitCount[n, b] gives a list of the counts of digits 1, 2, ..., b-1, 0 in the base-b representation of n.
DigitCount[n, b, d] gives the number of d digits in the base-b representation of n.
The sign of n is discarded; DigitCount[0] is a list of zeros.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= DigitCount[2147, 2, 1]
Out[1]= 5

In[2]:= DigitCount[2147, 2]
Out[2]= {5, 7}

In[3]:= DigitCount[100!]
Out[3]= {15, 19, 10, 10, 14, 19, 7, 14, 20, 30}

Implementation notes

builtin_digitcount tallies base-b digit occurrences of |n| (default base 10). The 3-argument form DigitCount[n, b, d] returns the scalar count of digit d (dc_count_one_digit); the 1/2-argument form returns the histogram {c(1), c(2), ..., c(b-1), c(0)} — digit 0 last, matching Mathematica — built by dc_build_histogram into a calloc'd int64 array. Validates arity (DigitCount::argb), numeric non-integer n (::int), base >= 2 (::base, also for fractional bases), digit in [0, base) (::digit), and caps the list-form base to avoid OOM (::ovfl); symbolic n returns NULL.

  • Protected (intentionally not Listable). DigitCount[{1,2,3}] is left

Attributes: 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]:= DigitCount[1234567890]
Out[1]= {1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

In[1]:= DigitCount[100!]
Out[1]= {15, 19, 10, 10, 14, 19, 7, 14, 20, 30}

In[1]:= DigitCount[255, 2]
Out[1]= {8, 0}

In[1]:= DigitCount[2^1000, 10, 0]
Out[1]= 28

Notes

DigitCount[n] tallies how often each digit appears in the base-10 expansion of n, in the order 1, 2, ..., 9, 0 (note that 0 is reported last). The pandigital number 1234567890 therefore gives ten ones. The distribution of the 158 digits of 100! shows the histogram for a large factorial. With a base argument, DigitCount[n, b] works in any radix — DigitCount[255, 2] = {8, 0} recovers the binary population count (255 is 11111111). The three-argument form DigitCount[n, b, d] returns just the count of digit d; here 2^1000 (a 302-digit number) contains 28 zeros. The sign of n is ignored and DigitCount[0] is all zeros.