How to avoid InexactError when computing row of Pascals Triangle - julia

Question

I wrote a function that computes a row of Pascals Triangle.
function calc_row(s, prev::Int64, num::Int64, den::Int64)
c = 1
next_num = num
next_den = den
if prev > 0
c = convert(Int64, round(prev * (num / den)))
next_num = num - 1
next_den = den + 1
end
s = push!(s, c)
if next_num > 0
calc_row(s, c, next_num, next_den)
else
s
end
end
function row(r)
s = []
calc_row(s, 0, r, 1)
end
With bigger inputs, like row(392) it dies with:
ERROR: LoadError: InexactError()
in calc_row(::Array{Any,1}, ::Int64, ::Int64, ::Int64) at /var/tmp/148-3.julia:17
in calc_row(::Array{Any,1}, ::Int64, ::Int64, ::Int64) at /var/tmp/148-3.julia:26 (repeats 10 times)
in row(::Int64) at /var/tmp/148-3.julia:34
in include_from_node1(::String) at ./loading.jl:488
in include_from_node1(::String) at /Applications/Julia-0.5.app/Contents/Resources/julia/lib/julia/sys.dylib:?
in process_options(::Base.JLOptions) at ./client.jl:262
in _start() at ./client.jl:318
in _start() at /Applications/Julia-0.5.app/Contents/Resources/julia/lib/julia/sys.dylib:?
while loading /var/tmp/148-3.julia, in expression starting on line 37
The offending line is:
c = convert(Int64, round(prev * (num / den)))
How can I avoid this error while still working with integers when computing an entry in the triangle?

Answer 1

Essentially, the code in the question is correct. To do large row number BigInts are better because Int64 is not enough to hold such numbers. Additionally, floating-point numbers for integer calculations are a source of trouble and rounding errors. So, a little touched up version:
function calc_row(s, prev, num, den)
c = one(den)
next_num = num
next_den = den
if prev > 0
c = (prev * num) ÷ den
next_num = num - 1
next_den = den + 1
end
s = push!(s, c)
return next_num > 0 ? calc_row(s, c, next_num, next_den) : s
end
function row{T}(r::T)
s = Vector{T}(0)
calc_row(s, zero(T), r, one(T))
end
And row(BigInt(392)) gives:
393-element Array{BigInt,1}:
1
392
76636
9962680
968870630
75184360888
4849391277276
267409290432648
12869072102071185
549080409688370560
21029779691064592448
730306894726061301376
23187243907552446318688
677780975759225353930880
18348499272339029224271680
462382181662943536451646336
10894880155433107077641916792
⋮
10894880155433107077641916792
462382181662943536451646336
18348499272339029224271680
677780975759225353930880
23187243907552446318688
730306894726061301376
21029779691064592448
549080409688370560
12869072102071185
267409290432648
4849391277276
75184360888
968870630
9962680
76636
392
1