Explain how Inigo Quilez calculates SDF box normals - intersection

Question

Inigo Quilez's website has a page of 3D ray-surface intersectors for use with signed distance functions, one of which is for a basic 3D box:
// axis aligned box centered at the origin, with size boxSize
vec2 boxIntersection( in vec3 ro, in vec3 rd, vec3 boxSize, out vec3 outNormal )
{
vec3 m = 1.0/rd; // can precompute if traversing a set of aligned boxes
vec3 n = m*ro; // can precompute if traversing a set of aligned boxes
vec3 k = abs(m)*boxSize;
vec3 t1 = -n - k;
vec3 t2 = -n + k;
float tN = max( max( t1.x, t1.y ), t1.z );
float tF = min( min( t2.x, t2.y ), t2.z );
if( tN>tF || tF<0.0) return vec2(-1.0); // no intersection
outNormal = (tN>0.0) ? step(vec3(tN),t1)) : // ro ouside the box
step(t2,vec3(tF))); // ro inside the box
outNormal *= -sign(rd);
return vec2( tN, tF );
}
In addition to calculating the intersection, it also calculates the surface normal at the point of intersection. Calculating the normal is the part I'm interested in. I would like to understand how it does this, but the page doesn't break down the math at all, and I haven't found any other sources that do (also, not understanding the process limits my understanding of what to search for).
Some parts make sense conceptually, like the calculation of near/far intersection points for the ray. But the calculation of constants that make up that calculation are lost on me. For example, it appears to do ray_origin/ray_direction, dividing a position by a (probably normalized) direction. What sort of result does that produce? I'd have assumed it would be nonsensical.
I'd like to understand how this works, rather than treat it like a black box.
I found another version, modified to only return normals, but shares many of the same calculations. It may be easier to explain, I just wish I knew how it worked.
vec3 boxNormal( in vec3 ro, in vec3 rd, vec3 boxSize)
{
vec3 m = 1.0/rd;
vec3 n = m*ro;
vec3 k = abs(m)*boxSize;
vec3 t1 = -n - k;
return -sign(rd)*step(t1.yzx,t1.xyz)*step(t1.zxy,t1.xyz);
}