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FSINCOS—Sine and Cosine

INSTRUCTION SET REFERENCE, A-L

3-382 Vol. 2A

FSINCOS—Sine and Cosine

Description

Computes both the approximate 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.

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. 

However, even within the range -2

63

 to +2

63

, inaccurate results can occur because the finite approximation of π 

used internally for argument reduction is not sufficient in all cases. Therefore, for accurate results it is safe to apply 
FSINCOS only to arguments reduced accurately in software, to a value smaller in absolute value than 3π/8. See the 

sections titled “Approximation of Pi” and “Transcendental Instruction Accuracy” 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.

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 

approximate sine, and push the approximate cosine onto the 

register stack.

Table 3-36.  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.