# Strange result from array arithmetic

**URL:** <https://discourse.julialang.org/t/strange-result-from-array-arithmetic/42772>\
**Category:** New to Julia\
**Created:** [July 9, 2020, 6:11am UTC](https://discourse.julialang.org/t/strange-result-from-array-arithmetic/42772 "2020-07-09T06:11:23Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![billmclean](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/billmclean/32/3790_2.png) [@billmclean](https://discourse.julialang.org/u/billmclean)\
**Post date:** [July 9, 2020, 6:11am UTC](https://discourse.julialang.org/t/strange-result-from-array-arithmetic/42772/1 "2020-07-09T06:11:23Z")

</div>

I get strange output from this function:

```julia
function foo(n)
           t = range(-1, 1, length=n)
           x = (t .- 1) ./ (t .+ 1)
           return x[1]
end

```

For example

```julia
julia> for n=100:110
           println("foo($n) = ", foo(n))
       end
foo(100) = -Inf
foo(101) = -Inf
foo(102) = -6.338253001141147e29
foo(103) = -Inf
foo(104) = -4.056481920730334e31
foo(105) = -Inf
foo(106) = 2.535301200456459e30
foo(107) = -Inf
foo(108) = -Inf
foo(109) = -Inf
foo(110) = -Inf

```

I am using the julia version packaged in Fedora 32:

```julia
julia> versioninfo()
Julia Version 1.4.2
Commit 44fa15b150* (2020-05-23 18:35 UTC)
Platform Info:
  OS: Linux (x86_64-redhat-linux)
  CPU: AMD Ryzen 7 1700 Eight-Core Processor
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-8.0.1 (ORCJIT, znver1)

```

If I define `g(t)=(t-1)/(t+1)` and do `x = g.(t)` then `x[1]` is alway `-Inf`, as expected.

---

<div class="post-metadata">

**Author:** ![jishnub](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jishnub/32/33620_2.png) [@jishnub](https://discourse.julialang.org/u/jishnub)\
**Post date:** [July 9, 2020, 7:13am UTC](https://discourse.julialang.org/t/strange-result-from-array-arithmetic/42772/2 "2020-07-09T07:13:35Z")

</div>

Looks like this is an issue with `StepRangeLen` not choosing the reference value to be the first one.

```julia
julia> s = range(-1, 1, length=102);

julia> b = Base.broadcasted(+,s,1)
3.1554436208840472e-30:0.019801980198019802:2.0

julia> b.offset
52

julia> b.ref
Base.TwicePrecision{Float64}(1.00990099009901, -8.7938457396052e-18)

julia> s[52] + 1
1.00990099009901

```

So it chooses the reference value to be the `52`nd one (I’m not sure how this works). Subsequently it tries to work backwards and evaluate the first value, which then isn’t zero anymore because the step size isn’t precise.

```julia
julia> s[1] + 1
0.0

julia> b[1]
3.1554436208840472e-30

```

When you evaulate `g.(t)`, it converts the range into an array, in which case each value is independently added to `1`, and the first term evaluates to zero.

---

<div class="post-metadata">

**Author:** ![billmclean](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/billmclean/32/3790_2.png) [@billmclean](https://discourse.julialang.org/u/billmclean)\
**Post date:** [July 9, 2020, 7:21am UTC](https://discourse.julialang.org/t/strange-result-from-array-arithmetic/42772/3 "2020-07-09T07:21:39Z")

</div>

Thanks jishnub. So defining

```julia
t = collect( range(-1, 1, length=102) );
x = (t .- 1) ./ (t .+ 1);

```

produces `x[1]` equal to `-Inf`.

---

<div class="post-metadata">

**Author:** ![bernhard](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bernhard/32/2619_2.png) [@bernhard](https://discourse.julialang.org/u/bernhard)\
**Post date:** [July 9, 2020, 8:25am UTC](https://discourse.julialang.org/t/strange-result-from-array-arithmetic/42772/4 "2020-07-09T08:25:47Z")

</div>

I note that you can also do this  
`t = range(-1, 2/n, length=n)`  
But this seems to fail for n=110 (it works for 100 to 109 though)

Your `collect` approach seems to work t hough.