How to use SO_KEEPALIVE option properly to detect that the client at the other end is down?

To modify the number of probes or the probe intervals, you write values to the /proc filesystem like

 echo 600 > /proc/sys/net/ipv4/tcp_keepalive_time
 echo 60 > /proc/sys/net/ipv4/tcp_keepalive_intvl
 echo 20 > /proc/sys/net/ipv4/tcp_keepalive_probes

Note that these values are global for all keepalive enabled sockets on the system, You can also override these settings on a per socket basis when you set the setsockopt, see section 4.2 of the document you linked.

You can't "check" the status of the socket from userspace with keepalive. Instead, the kernel is simply more aggressive about forcing the remote end to acknowledge packets, and determining if the socket has gone bad. When you attempt to write to the socket, you will get a SIGPIPE if keepalive has determined remote end is down.

You'll get the same result if you enable SO_KEEPALIVE, as if you don't enable SO_KEEPALIVE - typically you'll find the socket ready and get an error when you read from it.

You can set the keepalive timeout on a per-socket basis under Linux (this may be a Linux-specific feature). I'd recommend this rather than changing the system-wide setting. See the man page for tcp for more info.

Finally, if your client is a web browser, it's quite likely that it will close the socket fairly quickly anyway - most of them will only hold keepalive (HTTP 1.1) connections open for a relatively short time (30s, 1 min etc). Of course if the client machine has disappeared or network down (which is what SO_KEEPALIVE is really useful for detecting), then it won't be able to actively close the socket.

As already discussed, SO_KEEPALIVE makes the kernel more aggressive about continually verifying the connection even when you're not doing anything, but does not change or enhance the way the information is delivered to you. You'll find out when you try to actually do something (for example "write"), and you'll find out right away since the kernel is now just reporting the status of a previously set flag, rather than having to wait a few seconds (or much longer in some cases) for network activity to fail. The exact same code logic you had for handling the "other side went away unexpectedly" condition will still be used; what changes is the timing (not the method).

Virtually every "practical" sockets program in some way provides non-blocking access to the sockets during the data phase (maybe with select()/poll(), or maybe with fcntl()/O_NONBLOCK/EINPROGRESS&EWOULDBLOCK, or if your kernel supports it maybe with MSG_DONTWAIT). Assuming this is already done for other reasons, it's trivial (sometimes requiring no code at all) to in addition find out right away about a connection dropping. But if the data phase does not already somehow provide non-blocking access to the sockets, you won't find out about the connection dropping until the next time you try to do something.

(A TCP socket connection without some sort of non-blocking behaviour during the data phase is notoriously fragile, as if the wrong packet encounters a network problem it's very easy for the program to then "hang" indefinitely, and there's not a whole lot you can do about it.)