# Interval times Int64 and Interval times BigInt discrepancy
**URL:** https://discourse.julialang.org/t/interval-times-int64-and-interval-times-bigint-discrepancy/51902
**Category:** General Usage
**Tags:** bug, intervals
**Created:** [December 15, 2020, 11:30pm UTC](https://discourse.julialang.org/t/interval-times-int64-and-interval-times-bigint-discrepancy/51902 "2020-12-15T23:30:16Z")
**Posts on this page:** 8
**Page:** 1
### Author:  [@gmouts](https://discourse.julialang.org/u/gmouts)
#### Post date: [December 15, 2020, 11:30pm UTC](https://discourse.julialang.org/t/interval-times-int64-and-interval-times-bigint-discrepancy/51902/1 "2020-12-15T23:30:16Z")
I want to get the positive root of some polynomials with ridiculous precision. The polynomials I care I about are of the form \sum\_{k=0}^{n-1} a\_k x^k - x^n, with a\_k's being natural numbers. I am trying to write a program that does that efficiently and I found a weird bug.
The following is a minimal example. Unfortunately, I couldn’t minimise it any more.
```julia
using IntervalArithmetic
struct CauchyPolynomial{T,S,I<:Union{Int,Int128,BigInt}}
c::NTuple{T,I}
d::NTuple{S,I}
end
function CauchyPolynomial(ar::NTuple{N,T}) where N where T <:Union{Int,Int128,BigInt}
d = zeros(T,length(ar)-1)
for i in 2:length(ar)
d[i-1] = (i-1)*ar[i]
end
CauchyPolynomial(ar, tuple(d...))
end
@generated function pval_g(c::NTuple{N,I}, x::R) where I<:Union{Int,Int128,BigInt} where R<:Real where N
r = :(-one(R))
for i in N:-1:1
r = :(muladd(x, $r, c[$i] ) )
end
return r
end
@generated function dval_g(d::NTuple{N,I}, x::R) where I<:Union{Int,Int128,BigInt} where R<:Real where N
r = :(-one(R)*(N+1))
for i in N:-1:1
r = :(muladd(x, $r, d[$i] ) )
end
return r
end
function pval(p::CauchyPolynomial{M,N}, x::R) where M where N where R<:Real
return pval_g(p.c, x)
end
function dval(p::CauchyPolynomial{M,N}, x::R) where M where N where R<:Real
return dval_g(p.d, x)
end
function root(p::CauchyPolynomial{M,N}, bts::Int) where M where N
println("root called: ",p," - ",bts)
m = max(p.c...)
x = @biginterval m
while -log2(diam(x)) > bts
for i in 1:100
pt = pval(p,x)
x = x - pt/dval(p,x)
if 0 in pt
return x
end
end
end
throw(ErrorException("Newton method timed out, p: "*string(p)))
end
setprecision(8384);
ts = (832152526037543613, 4191427560420539572, 1948805851146604192, 41780545826284041, 2952882476324826786);
tb = map(big, ts);
ps = CauchyPolynomial(ts);
pb = CauchyPolynomial(tb);
root(pb, 8303)
root(ps, 8303)
```
When I execute this, the line `root(pb, 8303)` gives me the root but the line `root(ps, 8303)` times out.
The only difference between the polynomials `ps` and `pb` is that the coefficients of `ps` are `Int64` and the ones of `pb` are `BigInt`. Since integers are represented exactly, I expected that the difference in types wouldn’t matter. What is happening here?
Also, separate to this issue, any advice on how to improve the code is more than welcomed.
---
### Author:  [@Oscar\_Smith](https://discourse.julialang.org/u/Oscar_Smith)
#### Post date: [December 15, 2020, 11:54pm UTC](https://discourse.julialang.org/t/interval-times-int64-and-interval-times-bigint-discrepancy/51902/2 "2020-12-15T23:54:34Z")
For relatively short polynomials, the best way to evaluate this will almost certainly be
`pval_g(c,x) = evalpoly(x, tuple(c... ,-1))`.
That said, `BigInt` will always be way slower since `Int` is doing the computation modulo `2^64`.
---
### Author:  [@gmouts](https://discourse.julialang.org/u/gmouts)
#### Post date: [December 16, 2020, 12:27am UTC](https://discourse.julialang.org/t/interval-times-int64-and-interval-times-bigint-discrepancy/51902/3 "2020-12-16T00:27:41Z")
I think my function is faster since it is a generated function that takes into account that the highest order coefficient is always -1. If it is not, then I’m very curious to see why it is not.
---
### Author:  [@JeffreySarnoff](https://discourse.julialang.org/u/JeffreySarnoff)
#### Post date: [December 16, 2020, 12:37am UTC](https://discourse.julialang.org/t/interval-times-int64-and-interval-times-bigint-discrepancy/51902/4 "2020-12-16T00:37:54Z")
(without looking at your code)
Ints (the default Integer type) are bounded by `(typemin(Int), typemax(Int))` and they will wrap around:
```julia
julia> 0 > typemax(Int) + 2
true
```
So your evaluation logic may be causing the root finder to bounce back and forth ad infinitum when Ints are used with your specific calculation.
BigInts grow and grow, allowing the root finder to utilize whatever integer precision is required in this case.
---
### Author:  [@gmouts](https://discourse.julialang.org/u/gmouts)
#### Post date: [December 16, 2020, 12:46am UTC](https://discourse.julialang.org/t/interval-times-int64-and-interval-times-bigint-discrepancy/51902/5 "2020-12-16T00:46:30Z")
The “point” to be evaluated is `Interval{BigFloat}`. So the result of any computation is also `Interval{BigFloat}`.
---
### Author:  [@dpsanders](https://discourse.julialang.org/u/dpsanders)
#### Post date: [December 16, 2020, 6:14am UTC](https://discourse.julialang.org/t/interval-times-int64-and-interval-times-bigint-discrepancy/51902/6 "2020-12-16T06:14:49Z")
There was a recent thread about special methods to find roots of polynomials with integer coefficients.
---
### Author:  [@gmouts](https://discourse.julialang.org/u/gmouts)
#### Post date: [December 16, 2020, 12:39pm UTC](https://discourse.julialang.org/t/interval-times-int64-and-interval-times-bigint-discrepancy/51902/7 "2020-12-16T12:39:28Z")
I have seen the that thread, but it was not very useful to me.
Regardless, the integer type should not affect the result of the product. Am I missing something here? Is this not a bug?
---
### Author:  [@gmouts](https://discourse.julialang.org/u/gmouts)
#### Post date: [December 16, 2020, 1:47pm UTC](https://discourse.julialang.org/t/interval-times-int64-and-interval-times-bigint-discrepancy/51902/8 "2020-12-16T13:47:22Z")
I was an idiot, it overflows when I compute the coefficients of the derivative. 🤦♂️