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.

ST(0)
ST(1)		−∞	−F	±0	+0<+F<+1	+1	+F>+1	+∞	NaN
	−∞	*	*	+∞	+∞	*	−∞	−∞	NaN
	−F	*	*	**	+F	−0	−F	−∞	NaN
	−0	*	*	*	+0	−0	−0	*	NaN
	+0	*	*	*	−0	+0	+0	*	NaN
	+F	*	*	**	−F	+0	+F	+∞	NaN
	+∞	*	*	−∞	−∞	*	+∞	+∞	NaN
	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN

Table 3-48. FYL2X Results

F Meansfinitefloating-pointvalue.

* Indicatesfloating-pointinvalid-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.
C1	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.
#IA	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.