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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 register 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 3-48. FYL2X Results

					ST(0)
		- inf	- F	+-0	+0<+F<+1	+ 1	+ F > + 1	+ inf	NaN
	- inf	*	*	+ inf	+ inf	*	- inf	- inf	NaN
ST(1)	- F	*	*	**	+ F	- 0	- F	- inf	NaN
	- 0	*	*	*	+ 0	- 0	- 0	*	NaN
	+ 0	*	*	*	- 0	+ 0	+ 0	*	NaN
	+ F	*	*	**	- F	+ 0	+ F	+ inf	NaN
	+ inf	*	*	- inf	- inf	*	+ inf	+ inf	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 inf 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). Source operand in register ST(0) is +-0.
#Z
#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.