image/svg+xml FPTAN—Partial Tangent Description Computes the approximate tangent of the source operand in register ST(0), stores the result in ST(0), and pushes a 1.0 onto the FPU register stack. The source operand must be given in radians and must be less than ±2 63 . The following table shows the unmasked results obtained when computing the partial tangent 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 2 π . 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 FPTAN only to arguments reduced accurately in software, to a value smaller in absolute value than 3 π /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. The value 1.0 is pushed onto the register stack after the tangent has been computed to maintain compatibility with the Intel 8087 and Intel287 math coprocessors. This operation also simplifies the calculation of other trigonometric functions. For instance, the cotangent (which is the reciprocal of the tangent) can be computed by executing a FDIVR instruction after the FPTAN instruction. This instruction’s operation is the same in non-64-bit modes and 64-bit mode. OpcodeInstruction64-Bit Mode Compat/ Leg Mode Description D9 F2FPTANValidValidReplace ST(0) with its approximate tangent and push 1 onto the FPU stack. Table 3-33. FPTAN Results ST(0) SRCST(0) DEST − ∞ * − F − F to + F − 0 - 0 + 0 + 0 + F − F to + F + ∞ * NaN NaN NOTES: FMeans finite floating-point value. *Indicates floating-point invalid-arithmetic-operand (#IA) exception. image/svg+xml Operation IF ST(0) < 2 63 THEN C2 := 0; ST(0) := fptan(ST(0)); // approximation of tan TOP := TOP − 1; ST(0) := 1.0; ELSE (* Source operand is out-of-range *) C2 := 1; FI; FPU Flags Affected C1Set to 0 if stack underflow occurred; set to 1 if stack overflow occurred. Set if result was rounded up; cleared otherwise. C2Set to 1 if outside range ( − 2 63 < source operand < + 2 63 ); otherwise, set to 0. C0, C3 Undefined. Floating-Point Exceptions #ISStack underflow or overflow occurred. #IASource operand is an SNaN value, ∞ , or unsupported format. #DSource operand is a denormal value. #UResult is too small for destination format. #PValue cannot be represented exactly in destination format. Protected Mode Exceptions #NMCR0.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. This UNOFFICIAL reference was generated from the official Intel® 64 and IA-32 Architectures Software Developer’s Manual by a dumb script. There is no guarantee that some parts aren't mangled or broken and is distributed WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE .