FCOS— Cosine
INSTRUCTION SET REFERENCE, A-L
3-330 Vol. 2A
FCOS— Cosine
Description
Computes the approximate cosine of the source operand in register ST(0) and stores the result in ST(0). 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 cosine of various classes of numbers.
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
FCOS 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)| < 2
63
THEN
C2 ← 0;
ST(0) ← FCOS(ST(0)); // approximation of cosine
ELSE (* Source operand is out-of-range *)
C2 ← 1;
FI;
Opcode
Instruction
64-Bit
Mode
Compat/
Leg Mode
Description
D9 FF
FCOS
Valid
Valid
Replace ST(0) with its approximate cosine.
Table 3-23. FCOS Results
ST(0) SRC
ST(0) DEST
−
∞
*
−
F
−1 to +1
− 0
+ 1
+ 0
+ 1
+ F
− 1 to + 1
+
∞
*
NaN
NaN
NOTES:
F Means finite floating-point value.
* Indicates floating-point invalid-arithmetic-operand (#IA) exception.