Instead, it's handled by hardware
Hardware is a big space. Every compiled programming language will provide a maths library or attempt to use maths routines offered by the OS. The amount of work done in software and delegated to hardware will vary enormously from platform to platform. Check out some of these well known platforms:
ARM A9 - FPU is optional?:
Cortex-A9 Processor - ARM
Optional NEON™ media and/or floating point processing engine
Some embedded x86 have no FPU:
Using software floating point on x86 linux - Stack Overflow
Partial support on MIPS:
Floating point - LinuxMIPS
The conceptual association in the JLS is certainly from the point of view of use of Java double: it's telling you you can do anything with a Java double you might expect to do with an IEEE754-1985 (not a -2008 one!) double. The nitty-gritty of floating point computation may be delegated by the JVM to whatever support exists on the target platform - but I suspect it could be difficult to guarantee that the results of double computations are identical across all JVMs unless they're carried out in software by the JVM itself.
much more likely to trust hardware
Are you assuming 'black box so it must work'?
This is a great James Gosling article which touches on a lot of the issue brought up by this discussion. You'll never use floating point again:
James Gosling: on the Java Road - Transcendental Meditation