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Julia DISCUSSION
I compute an array position as n / 2 and then use it as an index, and Julia refuses with an error about an invalid index of type Float64. Wrapping it in Int(...) works for even n but throws InexactError for odd n. In C the same code simply truncates.
What is the intended way to go from a floating-point value to an integer in Julia, and which rounding does each option use?
/ always produces a floating-point result for integers: 10 / 2 is 5.0, not 5. Array indices must be integers, hence the first error. For an integer quotient, use integer division: n ÷ 2, which is the same as div(n, 2) and truncates toward zero, so 7 ÷ 2 == 3. You can type the symbol in the REPL as \div followed by Tab. Then no conversion is needed at all, which is the best fix for an index calculation.
Int(x) is a lossless conversion, not a rounding operation. Int(4.0) gives 4, but Int(3.5) throws InexactError because there is no integer equal to 3.5. Julia makes you say which rounding you want: trunc(Int, x) toward zero (the C cast behaviour), floor(Int, x) down, ceil(Int, x) up, and round(Int, x) to nearest.
Without the type argument, these return a floating-point value: round(3.7) is 4.0.
Watch the tie rule of round. The default mode rounds halves to the nearest even integer, so round(Int, 2.5) is 2 and round(Int, 3.5) is 4. That avoids a systematic upward bias when many values are rounded, but it surprises people who expect 3. For the schoolbook rule, pass the mode: round(Int, 2.5, RoundNearestTiesAway) gives 3.
For negative numbers the variants differ too: trunc(Int, -3.7) is -3, floor(Int, -3.7) is -4.
The integer division family has the same distinctions. div(-7, 2) is -3 and fld(-7, 2) is -4 (floored), with cld rounding up. The matching remainders are rem(-7, 2) == -1, which is what % does, and mod(-7, 2) == 1.
For wrapping an index into a circular buffer of length N with 1-based indexing, mod1(i, N) returns a value in 1 to N directly, which avoids the usual off-by-one.
Two range limits to keep in mind. The conversion also throws when the value does not fit: round(Int, 1e20) is an InexactError, since Int is 64 bits on a 64-bit system and tops out near 9.22 × 10^18. NaN and Inf fail the same way, so check with isfinite(x) if the input comes from a measurement.
Integer arithmetic itself is not checked: typemax(Int) + 1 silently wraps to typemin(Int). If that can happen, use a wider type such as Int128 or BigInt, or the checked functions like Base.checked_add.
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