The point of test %eax %eax

CMP subtracts the operands and sets the flags. Namely, it sets the zero flag if the difference is zero (operands are equal).

TEST sets the zero flag, ZF, when the result of the AND operation is zero. If two operands are equal, their bitwise AND is zero when both are zero. TEST also sets the sign flag, SF, when the most significant bit is set in the result, and the parity flag, PF, when the number of set bits is even.

JE [Jump if Equals] tests the zero flag and jumps if the flag is set. JE is an alias of JZ [Jump if Zero] so the disassembler cannot select one based on the opcode. JE is named such because the zero flag is set if the arguments to CMP are equal.

So,

TEST %eax, %eax
JE   400e77 <phase_1+0x23>

jumps if the %eax is zero.

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