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Range

Status: Stable

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

Description

Range[n]
    generates the list {1, 2, 3, ..., n}.
Range[n, m]
    generates the list {n, n + 1, ..., m - 1, m}.
Range[n, m, d]
    uses step d.

Examples

No verified examples yet for this function.

Implementation notes

builtin_range (in src/list.c) generates the arithmetic sequence for Range[imax] (origin 1, step 1), Range[imin, imax], and Range[imin, imax, di]. Bounds may be integers, reals, or rationals (parsed via is_rational); a double view of each is used only for the loop-termination test (val <= max_val + 1e-14, or the reversed test for negative step, with a 1,000,000-element cap). The element values themselves are built exactly: a running curr_e starts at imin and is advanced each step by evaluate(Plus[curr_e, di]), so integer and rational ranges stay exact while any real bound promotes the elements to EXPR_REAL. A zero step, or an empty oriented range, yields {}; the result is wrapped as List[...].

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]:= Range[5]
Out[1]= {1, 2, 3, 4, 5}

In[1]:= Range[2, 10, 2]
Out[1]= {2, 4, 6, 8, 10}

In[1]:= Range[0, 1, 1/4]
Out[1]= {0, 1/4, 1/2, 3/4, 1}

A negative step counts down, and Range chains naturally with the functional operators it is built to feed — here the exact triangular numbers and the sum of the first hundred integers:

In[1]:= Range[10, 1, -1]
Out[1]= {10, 9, 8, 7, 6, 5, 4, 3, 2, 1}

In[2]:= Map[#^2 &, Range[5]]
Out[2]= {1, 4, 9, 16, 25}

In[3]:= Total[Range[100]]
Out[3]= 5050

Notes

Range[n] produces the integers 1 through n. Range[n, m] runs from n to m in unit steps, and Range[n, m, d] uses step d. The step may be an exact rational, in which case the result stays exact rather than being converted to floating point. Range is the most direct way to build the index list that Map, Select, or Fold then consume.