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 3-48. FYL2X Results

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

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):

logbx ← (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.