I am getting some behavior I can not explain. The context is that a chamber gets 9/16’ths of its content emptied, initially air. Then the 9/16ths that were removed are replaced with some pure gas. This process is repeted, and I wanted to find out how fast one starts getting pure gas. So I wrote the following script, and included a sanity-check that the air part a plus the gas part g always sum to 16. But the boolean comparison failed in the following three versions of the script:
Normal division, comparison with 16 as Int:
julia> begin
a = 16
g = 0
counter = 0
for i in 1:2
a *= 7/16
g *= 7/16
g += 9
counter +=1
if a+g !== 16
println("Error! $a+$g=$(a+g) does not equal 16.")
#error("Gas parts do not sum to 16")
end
println("Iteration $counter:\nGas to air ratio = $(round(g/a, sigdigits=3))\n\n")
end
end
Error! 7.0+9.0=16.0 does not equal 16.
Iteration 1:
Gas to air ratio = 1.29
Error! 3.0625+12.9375=16.0 does not equal 16.
Iteration 2:
Gas to air ratio = 4.22
Even though
julia> 0.005+15.995
16.0
julia> 0.005+15.995 == 16
true
Rational division, comparison with 16 as Int:
julia> begin
a = 16
g = 0
counter = 0
for i in 1:2
a *= 7//16
g *= 7//16
g += 9
counter +=1
if a+g !== 16
println("Error! $a+$g=$(a+g) does not equal 16.")
#error("Gas parts do not sum to 16")
end
println("Iteration $counter:\nGas to air ratio = $(round(g/a, sigdigits=3))\n\n")
end
end
Error! 7//1+9//1=16//1 does not equal 16.
Iteration 1:
Gas to air ratio = 1.29
Error! 49//16+207//16=16//1 does not equal 16.
Iteration 2:
Gas to air ratio = 4.22
Even though
julia> 16//1==16
true
Rational division, comparison with 16 as float:
julia> begin
a = 16
g = 0
counter = 0
for i in 1:2
a *= 7//16
g *= 7//16
g += 9
counter +=1
if a+g !== 16.0
println("Error! $a+$g=$(a+g) does not equal 16.")
#error("Gas parts do not sum to 16")
end
println("Iteration $counter:\nGas to air ratio = $(round(g/a, sigdigits=3))\n\n")
end
end
Error! 7//1+9//1=16//1 does not equal 16.
Iteration 1:
Gas to air ratio = 1.29
Error! 49//16+207//16=16//1 does not equal 16.
Iteration 2:
Gas to air ratio = 4.22
The only successful version was without rationals, and where 16 was defined as a float as opposed to an int:
julia> begin
a = 16
g = 0
counter = 0
for i in 1:2
a *= 7/16
g *= 7/16
g += 9
counter +=1
if a+g !== 16.0
println("Error! $a+$g=$(a+g) does not equal 16.")
#error("Gas parts do not sum to 16")
end
println("Iteration $counter:\nGas to air ratio = $(round(g/a, sigdigits=3))\n\n")
end
end
Iteration 1:
Gas to air ratio = 1.29
Iteration 2:
Gas to air ratio = 4.22
I can not explain why they dont all evaluate to true. Can you help me understand?