I have used the avr-objdump to translate the .elf file generated by the Arduino into assembly code. However, I find that I cannot see how the mathmatical operations are operated in that file. For example, any instruction like ADD, SUB, MUL is absence...
Basically, I'm interested in how the floating arithmatic operation is done in AVR... So, is there any method to see how it works in assembly codes?
The AVR LibC is an open source library. Just download the original sources and look at how those operations are implemented. You should find everything you're looking for inside the \libm\libfp folder. It is not light reading though.
Furthermore be aware that a lot of numerical methods are used to calculate floating functions, Taylor sequences( gonio?), Newton Raphson so it wil be wise to read a book or two about that subject too.