Intel 253666-024US - Manual (Page 403)

Vol. 2A 3-357
INSTRUCTION SET REFERENCE, A-M
FPATAN—Partial Arctangent
There is no restriction on the range of source operands that FPATAN can accept.
This instruction’s operation is the same in non-64-bit modes and 64-bit mode.
IA-32 Architecture Compatibility
The source operands for this instruction are restricted for the 80287 math copro-
cessor to the following range:
0 ≤ |ST(1)| < |ST(0)| < +∞
Operation
ST(1) ← arctan(ST(1) / ST(0));
PopRegisterStack;
FPU Flags Affected
C1 Set to 0 if stack underflow occurred.
Set if result was rounded up; cleared otherwise.
C0, C2, C3 Undefined.
Table 3-35. FPATAN Results
ST(0)
- ∞ −F −0 +0 +F + ∞ NaN
- ∞ −3π/ 4 * −π/2 −π/2 −π/2 −π/2 −π/4 * NaN
ST(1) −F -p −π to −π/ 2 −π/2 −π/2 −π/ 2 to −0 -0 NaN
−0 -p -p -p * −0 * −0 −0 NaN
+0 +p +p +π * +0 * +0 +0 NaN
+F +p +π to +π/ 2 +π/ 2 +π/ 2 +π/ 2 to +0 +0 NaN
+ ∞ +3π/ 4 * +π/ 2 +π/ 2 +π/ 2 +π/ 2 +π/4 * NaN
NaN NaN NaN NaN NaN NaN NaN NaN
NOTES:
F Means finite floating-point value.
* Table 8-10 in the Intel® 64 and IA-32 Architectures Software Developer’s Manual, Volume 1,
specifies that the ratios 0/0 and •/• generate the floating-point invalid arithmetic-operation
exception and, if this exception is masked, the floating-point QNaN indefinite value is returned.
With the FPATAN instruction, the 0/0 or •/• value is actually not calculated using division.
Instead, the arctangent of the two variables is derived from a standard mathematical formula-
tion that is generalized to allow complex numbers as arguments. In this complex variable formu-
lation, arctangent(0,0) etc. has well defined values. These values are needed to develop a library
to compute transcendental functions with complex arguments, based on the FPU functions that
only allow floating-point values as arguments.