FYL2X—Compute y ∗ log2x

Opcode	Instruction	64-Bit Mode	Compat/Leg Mode	Description
D9 F1	FYL2X	Valid	Valid	Replace ST(1) with (ST(1) ∗ log₂ST(0)) and pop the register stack.

Description

Computes (ST(1) ∗ log₂ (ST(0))), stores the result in resister ST(1), and pops the FPU register stack. The source operand in ST(0) must be a non-zero positive number.

The following table shows the results obtained when taking the log of various classes of numbers, assuming that neither overflow nor underflow occurs.

Table 3-58. FYL2X Results

ST(0)

− ∞	− F	±0 + ∞****− ∞	+0<+F<+1 + ∞+ F + 0 − 0 − F − ∞	+ 1 −0 −0 +0 +0	+ F > + 1 − ∞− F − 0 + 0 + F + ∞	+ ∞− ∞− ∞+∞+∞	NaN NaN NaN NaN NaN NaN NaN
NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN

Notes: F Means finite floating-point value. * Indicates floating-point invalid-operation (#IA) exception. ** Indicates floating-point zero-divide (#Z) exception.

If the divide-by-zero exception is masked and register ST(0) contains ±0, the instruction returns ∞ with a sign that is the opposite of the sign of the source operand in register ST(1).

The FYL2X instruction is designed with a built-in multiplication to optimize the calculation of logarithms with an arbitrary positive base (b):

log_bx ← (log₂b)^-1 ∗ log₂x

This instruction’s operation is the same in non-64-bit modes and 64-bit mode.

Operation

ST(1) ← ST(1) ∗ log₂ST(0);
PopRegisterStack;

FPU Flags Affected

C1	Set to 0 if stack underflow occurred. Set if result was rounded up; cleared otherwise.
C0, C2, C3	Undefined.

Floating-Point Exceptions

#IS	Stack underflow occurred.
#IA	Either operand is an SNaN or unsupported format. Source operand in register ST(0) is a negative finite value (not -0).
#Z	Source operand in register ST(0) is ±0.
#D	Source operand is a denormal value.
#U	Result is too small for destination format.
#O	Result is too large for destination format.
#P	Value cannot be represented exactly in destination format.

Protected Mode Exceptions

#NM	CR0.EM[bit 2] or CR0.TS[bit 3] = 1.
#MF	If there is a pending x87 FPU exception.
#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.

Compatibility Mode Exceptions

Same exceptions as in protected mode.

64-Bit Mode Exceptions

Same exceptions as in protected mode.