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.

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):

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.