f2xm1

Compute 2^x - 1

F2XM1

Computes (2^ST(0)) - 1.

Details

Computes 2^ST(0) − 1 and stores the result back in ST(0). ST(0) must be in the range [−1, 1] for accurate results; values outside this range produce undefined behavior or reduced accuracy. This instruction is used as part of logarithm and exponential function approximations in transcendental math libraries.

Pseudocode Operation

if (ST(0) < -1 or ST(0) > 1) {
  undefined_behavior()
} else {
  ST(0) ← (2 ^ ST(0)) - 1
}

Example

F2XM1

Encoding

Binary Layout

Format Legacy

Opcode D9 F0

Extension x87 FPU

Operands

Reference (Intel® SDM)

Instruction Forms

Opcode	Instruction	Op/En	64/32-bit Mode	CPUID	Description
D9 F0	F2XM1		Valid Valid		Replace ST(0) with (2ST(0) – 1).

Description

Computes the exponential value of 2 to the power of the source operand minus 1. The source operand is located in register ST(0) and the result is also stored in ST(0). The value of the source operand must lie in the range –1.0 to +1.0. If the source value is outside this range, the result is undefined. The following table shows the results obtained when computing the exponential value of various classes of numbers, assuming that neither overflow nor underflow occurs. Table 3-18. Results Obtained from F2XM1 ST(0) SRC ST(0) DEST − 1.0 to −0 − 0.5 to − 0 − 0 − 0 + 0 + 0 + 0 to +1.0 + 0 to 1.0 Values other than 2 can be exponentiated using the following formula: xy := 2(y ∗ log2x) This instruction’s operation is the same in non-64-bit modes and 64-bit mode.

Operation

ST(0) := (2ST(0) − 1);

Exceptions

Protected Mode Exceptions

#NM CR0.EM[bit 2] or CR0.TS[bit 3] = 1. #UD If the LOCK prefix is used.

Real-Address Mode Exceptions

Same exceptions as in protected mode.

Virtual-8086 Mode Exceptions

Same exceptions as in protected mode. F2XM1—Compute 2x–1 Vol. 2A 3-307

Compatibility Mode Exceptions

Same exceptions as in protected mode.

64-Bit Mode Exceptions

Same exceptions as in protected mode. F2XM1—Compute 2x–1 Vol. 2A 3-308