# 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.

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.

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.