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FSINCOS - Sine and Cosine

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.

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 - 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.

Table 3-36. FSINCOS Results

SRC	DEST	DEST
ST(0)	ST(1) Cosine	ST(0) Sine
- inf	* *	* *
- F	- 1 to + 1 - 1 to + 1	- 1 to + 1 - 1 to + 1
- 0	+ 1 - 0	+ 1 - 0
+ 0	+ 1 + 0	+ 1 + 0
+ F	- 1 to + 1 - 1 to + 1	- 1 to + 1 - 1 to + 1
+ inf	* *	* *
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 -

2⁶³ to +2⁶³ can be reduced to the range of the instruction by subtracting an appropriate integer multiple of 2π.

However, even within the range -2⁶³ to +2⁶³, 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.

Operation

IF ST(0) < 263
   THEN
       C2 := 0;
       TEMP := fcos(ST(0)); // approximation of cosine
       ST(0) := fsin(ST(0)); // approximation of sine
       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. Set to 1 if outside range ( - 263 < source operand < +263); otherwise, set to 0.
C2
C0, C3	Undefined.

Floating-Point Exceptions

#IS	Stack underflow or overflow occurred. Source operand is an SNaN value, inf, or unsupported format.
#IA
#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.