Sine and Cosine


Hex Mnemonic Encoding Long Mode Legacy Mode Description
D9 FB FSINCOS None Valid Valid Compute the sine and cosine of ST(0); replace ST(0) with the sine, and push the cosine onto the register stack.


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 -263 to +263. The following table shows the results obtained when taking the sine and cosine of various classes of numbers, assuming that underflow does not occur.

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
+∞ * *

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 -263 to +263 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 theIntel®64 and IA-32 ArchitecturesSoftware 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.

Pseudo Code

IF ST(0) < 263
	C2 = 0;
	TEMP = cosine(ST(0));
	ST(0) = sine(ST(0));
	TOP = TOP - 1;
	ST(0) = TEMP;
	(* Source operand out of range *)
	C2 = 1;

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 (-263 < source operand <+263); otherwise, set to 0. C0, C3 Undefined.


Floating-Point Exceptions

Exception Description
#P Value cannot be represented exactly in destination format.
#U Result is too small for destination format.
#D Source operand is a denormal value.
#IA Source operand is an SNaN value, ∞, or unsupported format.
#IS Stack underflow or overflow occurred.

64-Bit Mode Exceptions

Same exceptions as in protected mode.

Compatibility Mode Exceptions

Same exceptions as in protected mode.

Virtual-8086 Mode Exceptions

Same exceptions as in protected mode.

Real-Address Mode Exceptions

Same exceptions as in protected mode.

Protected Mode Exceptions

Exception Description
#UD If the LOCK prefix is used.
#MF If there is a pending x87 FPU exception.
#NM CR0.EM[bit 2] or CR0.TS[bit 3] = 1.