There is no real reason why you should. Remember that EAX is only a 32-bit register, while all the FPU registers are 80 bits in width, because the FPU does calculations on 80-bit floats by default. Therefore, moving data from the FPU register to a general purpose register will cause data loss. If you really want to do something like that, try this (assuming that you’ve got some stack space available) :
sub esp, 4 ; or use space you already reserved fstp dword [esp] mov eax, [esp] ; or better, pop eax add esp, 4
This instruction sequence will round the float currently on the top of the FPU stack to a 32-bit one, then write it to a temporary stack location, load the float (binary32) bit pattern into EAX, and clean up the used stack space.
This is almost never what you want. The standard calling conventions return float / double / long double values in st(0), so that’s where a C compiler will expect a double foo() function to leave the value. (Or xmm0 with SSE/SSE2).
You only need this if you want to do integer manipulation / tests on FP bit-patterns. (i.e. to implement type-punning in C like memcpy from a float to uint32_t). e.g. for the famous but now mostly obsolete fast approximate inverse-sqrtf magic-number hack used in Quake source code.