# FYL2X—Compute y ∗ log2x

Opcode |
Instruction |
64-Bit Mode |
Compat/Leg Mode |
Description |

D9 F1 |
FYL2X |
Valid |
Valid |
Replace ST(1) with (ST(1) ∗ log_{2}ST(0)) and pop the register stack. |

## Description

Computes (ST(1) ∗ log_{2} (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 3-58. FYL2X Results

ST(0)

− ∞ |
− F |
±0 + ∞****− ∞ |
+0<+F<+1 + ∞+ F + 0 − 0 − F − ∞ |
+ 1 −0 −0 +0 +0 |
+ F > + 1 − ∞− F − 0 + 0 + F + ∞ |
+ ∞− ∞− ∞+∞+∞ |
NaN NaN NaN NaN 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):

log_{b}x ← (log_{2}b)^{-1} ∗ log_{2}x

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

## Operation

ST(1) ← ST(1) ∗ log_{2}ST(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.