# UB in various hypot() implementations (left-shifting a negative number)

Jeff Walden jwalden at mit.edu
Wed Nov 13 22:43:13 UTC 2019

```Hi all,

Just wanted to note here that I filed https://reviews.freebsd.org/D22354 to fix a bit of undefined behavior in the hypot() function implementations.

`hypot(x, y)` computes `sqrt(x*x + y*y)`, with IEEE-754-aware precision.  For very large or small `x` or `y`, the naive implementation would lose precision -- so in such cases the calculation is performed after multiplying the numbers by a very large (or very small) power of two, then the multiplication is undone at end.

Undoing the multiplication involves multiplying a quantity `w` by `2**k`, where `k` (which may be positive or negative) was computed depending on the particular `x` and `y` values provided.  Current algorithms generally take `t1=0.0`, extract the high word, add `k<<20` or `k<<23` to it to appropriately bump the exponent, then overwrite `t1`'s high word.  But it seems equally effective to take `t1=0.0`, then write `(1023+k)<<20` or `(127+k)<<23` to it for identical effect -- and `k` is never so negative to compute a negative value.  My changes do this.  (I wish there were named constants I could use for all these numbers, but as there don't seem to be any, magic numbers seems like the best I can do.)

Errors in these changes would most likely produce a power of two off by a factor of two, so *probably* testing any inputs that would happen to invoke these code paths should be adequate testing.  I'm fixing this in order to upstream a likely fix in the SpiderMonkey JavaScript engine for this, so the (double, double) algorithm/change is the only one I have (purely manually) tested.  Eyeballs on the other functions' changes especially appreciated!

Jeff
```