fpatan

Partial Arctangent

FPATAN

Computes arctan(ST(1)/ST(0)).

Details

Computes the two-argument arctangent of ST(1)/ST(0) and replaces both stack entries with the result in ST(0); the stack pointer is decremented. The result is in the range [-π/2, π/2] or [-π, π] depending on the signs of ST(1) and ST(0). The x87 status flags are updated accordingly.

Pseudocode Operation

ST(0) ← atan2(ST(1), ST(0)); pop(); TOS ← TOS - 1

Example

FPATAN

Encoding

Binary Layout
D9
+0
F3
+1
 
Format Legacy
Opcode D9 F3
Extension x87 FPU

Operands

Reference (Intel® SDM)

Instruction Forms

Opcode Instruction Op/En 64/32-bit Mode CPUID Description
D9 F3 FPATAN Valid Valid Replace ST(1) with arctan(ST(1)/ST(0)) and pop the register stack.

Description

Computes the arctangent of the source operand in register ST(1) divided by the source operand in register ST(0), stores the result in ST(1), and pops the FPU register stack. The result in register ST(0) has the same sign as the source operand ST(1) and a magnitude less than +π. The FPATAN instruction returns the angle between the X axis and the line from the origin to the point (X,Y), where Y (the ordinate) is ST(1) and X (the abscissa) is ST(0). The angle depends on the sign of X and Y independently, not just on the sign of the ratio Y/X. This is because a point (−X,Y) is in the second quadrant, resulting in an angle between π/2 and π, while a point (X,−Y) is in the fourth quadrant, resulting in an angle between 0 and −π/2. A point (−X,−Y) is in the third quadrant, giving an angle between −π/2 and −π. The following table shows the results obtained when computing the arctangent of various classes of numbers, assuming that underflow does not occur. Table 3-32. 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

Operation

ST(1) := arctan(ST(1) / ST(0));
PopRegisterStack;

Exceptions

Protected Mode Exceptions

#NM CR0.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. FPATAN—Partial Arctangent Vol. 2A 3-365