# FSINCOS (Sine and Cosine)

## Opcodes

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

D9 FB | FSINCOS | Valid | Valid | Compute the sine and cosine of ST(0); replace ST(0) with the sine, and push the cosine onto the register stack. |

## Description

Computes both the sine and the cosine of the source operand in register ST(0), stores the sine in ST(0), and pushes the cosine onto the top of the FPU register stack. (This instruction is faster than executing the FSIN and FCOS instructions in succession.)

The source operand must be given in radians and must be within the range −2^{63} to +2^{63}. The following table shows the results obtained when taking the sine and cosine of various classes of numbers, assuming that underflow does not occur.

## Table 3-46. FSINCOS Results

**SRC**

**DEST**

ST(0) | ST(1) Cosine | ST(0) Sine |

− ∞ | * | * |

− F | − 1 to + 1 | − 1 to + 1 |

− 0 | + 1 | − 0 |

+ 0 | + 1 | + 0 |

+ F | − 1 to + 1 | − 1 to + 1 |

+ ∞ | * | * |

NaN | NaN | NaN |

**NOTES:**

F Means finite floating-point value.

*

Indicates floating-point invalid-arithmetic-operand (#IA) exception.

If the source operand is outside the acceptable range, the C2 flag in the FPU status word is set, and the value in register ST(0) remains unchanged. The instruction does not raise an exception when the source operand is out of range. It is up to the program to check the C2 flag for out-of-range conditions. Source values outside the range − 2^{63} to +2^{63} can be reduced to the range of the instruction by subtracting an appropriate integer multiple of 2π or by using the FPREM instruction with a divisor of 2π. See the section titled “Pi” in Chapter 8 of the *Intel® 64 and IA-32 Architectures Software Developer’s Manual, Volume 1*, for a discussion of the proper value to use for π in performing such reductions.

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

## Operation

IF ST(0)

2

^{63}

THEN C2 ← 0; TEMP ← cosine(ST(0)); ST(0) ← sine(ST(0)); TOP ← TOP − 1; ST(0) ← TEMP; ELSE (* Source operand out of range *) C2 ← 1; FI;

## FPU Flags Affected

C1 | Set to 0 if stack underflow occurred; set to 1 of stack overflow occurs. Set if result was rounded up; cleared otherwise. |
---|---|

C2 | Set to 1 if outside range (−2^{63} source operand +2^{63}); otherwise, set to 0. |

C0, C3 | Undefined. |

## Floating-Point Exceptions

#IS | Stack underflow or overflow occurred. |

#IA | Source operand is an SNaN value, ∞, or unsupported format. |

#D

Source operand is a denormal value.

#U

Result is too small 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.