FCOS— CosineDescriptionComputes 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 −263 to +263. 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 −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 πused 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.OperationIF |ST(0)| < 263THENC2 := 0;ST(0) := FCOS(ST(0)); // approximation of cosineELSE (* Source operand is out-of-range *)C2 := 1;FI;OpcodeInstruction64-Bit ModeCompat/Leg ModeDescriptionD9 FFFCOSValidValidReplace ST(0) with its approximate cosine.Table 3-23. FCOS ResultsST(0) SRCST(0) DEST−∞*−F−1 to +1− 0+ 1+ 0+ 1+ F−1 to+ 1+∞*NaNNaN NOTES:FMeans finite floating-point value.* Indicates floating-point invalid-arithmetic-operand (#IA) exception.
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