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.