# Surprising benchmark results for a basic mixed precision example

**URL:** <https://discourse.julialang.org/t/surprising-benchmark-results-for-a-basic-mixed-precision-example/94410>\
**Category:** Numerics\
**Created:** [February 10, 2023, 1:44pm UTC](https://discourse.julialang.org/t/surprising-benchmark-results-for-a-basic-mixed-precision-example/94410 "2023-02-10T13:44:05Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![nvenkov1](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/nvenkov1/32/43679_2.png) [@nvenkov1](https://discourse.julialang.org/u/nvenkov1)\
**Post date:** [February 10, 2023, 1:44pm UTC](https://discourse.julialang.org/t/surprising-benchmark-results-for-a-basic-mixed-precision-example/94410/1 "2023-02-10T13:44:05Z")

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I started to experiment with mixed precision and I benchmarked a basic example as follows:

```julia
using BenchmarkTools
using Quadmath
using LinearAlgebra
a16 = Vector{Float16}(undef, 100_000_000);
a32 = Vector{Float32}(undef, 100_000_000);
a64 = Vector{Float64}(undef, 100_000_000);
a128 = Vector{Float128}(undef, 100_000_000);
@benchmark norm(a16)
@benchmark norm(a32)
@benchmark norm(a64)
@benchmark norm(a128)

```

I get the following median times:  
862.683 ms for a16  
25.218 ms for a32  
47.776 ms for a64  
1.143 s for a128

I tried it several times, including with zeros instead of undef, and I keep getting similar results. Aren’t these results surprising? Why is the time taken by norm(a16) larger (and by so much) than the time taken by norm(a32) and norm(a64)? Also, isn’t the time taken by norm(a128) a bit large compared to the times taken by norm(a32) and norm(a64)?

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<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [February 10, 2023, 1:47pm UTC](https://discourse.julialang.org/t/surprising-benchmark-results-for-a-basic-mixed-precision-example/94410/2 "2023-02-10T13:47:57Z")

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> [@nvenkov1](#):
>
> Why is the time taken by norm(a16) larger (and by so much) than the time taken by norm(a32) and norm(a64)?

There’s no hardware accelerator for that case on your CPU, so its a slow software thing.

> [@nvenkov1](#):
>
> Also, isn’t the time taken by norm(a128) a bit large compared to the times taken by norm(a32) and norm(a64)?

Again, no hardware accelerator, so it’s a slower software emulation. For this case, you might want to look into double-double arithmetic, i.e. DoubleDouble.jl