FYL2X

Calculate y × log2(x)

Opcodes

Hex Mnemonic Encoding Long Mode Legacy Mode Description
D9 F1 FYL2X None 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.

FYL2X Results
DEST
SRC
-∞ -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

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):

logbx = (log2b)-1 * log2x

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

Pseudo Code

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 are undefined.

Exceptions

Floating-Point Exceptions

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

64-Bit Mode Exceptions

Same exceptions as in protected mode.

Compatibility Mode Exceptions

Same exceptions as in protected mode.

Virtual-8086 Mode Exceptions

Same exceptions as in protected mode.

Real-Address Mode Exceptions

Same exceptions as in protected mode.

Protected Mode Exceptions

Exception Description
#UD If the LOCK prefix is used.
#MF If there is a pending x87 FPU exception.
#NM CR0.EM[bit 2] or CR0.TS[bit 3] = 1.