# 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 Means finite floating-point value.

> * 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.