Vol. 1 8-21

PROGRAMMING WITH THE X87 FPU

first be moved to the AX register in the integer unit. The FSTSW AX (store status word) instruction can be used for 
this purpose. When these flags are in the AX register, the TEST instruction can be used to control conditional 
branching as follows:
1. Check for an unordered result. Use the TEST instruction to compare the contents of the AX register with the 

constant 0400H (see Table 8-8). This operation will clear the ZF flag in the EFLAGS register if the condition code 
flags indicate an unordered result; otherwise, the ZF flag will be set. The JNZ instruction can then be used to 
transfer control (if necessary) to a procedure for handling unordered operands.

2. Check ordered comparison result. Use the constants given in Table 8-8 in the TEST instruction to test for a less 

than, equal to, or greater than result, then use the corresponding conditional branch instruction to transfer 
program control to the appropriate procedure or section of code.

If a program or procedure has been thoroughly tested and it incorporates periodic checks for QNaN results, then it 
is not necessary to check for the unordered result every time a comparison is made.
See Section 8.1.4, “Branching and Conditional Moves on Condition Codes,” for another technique for branching on 
x87 FPU condition codes.
Some non-comparison x87 FPU instructions update the condition code flags in the x87 FPU status word. To ensure 
that the status word is not altered inadvertently, store it immediately following a comparison operation.

8.3.7 Trigonometric 

Instructions

The following instructions perform four common trigonometric functions:

FSIN

Sine

FCOS

Cosine

FSINCOS

Sine and cosine

FPTAN

Tangent

FPATAN

Arctangent

These instructions operate on the top one or two registers of the x87 FPU register stack and they return their 
results to the stack. The source operands for the FSIN, FCOS, FSINCOS, and FPTAN instructions must be given in 
radians; the source operand for the FPATAN instruction is given in rectangular coordinate units.
The FSINCOS instruction returns both the sine and the cosine of a source operand value. It operates faster than 
executing the FSIN and FCOS instructions in succession.
The FPATAN instruction computes the arctangent of ST(1) divided by ST(0), returning a result in radians. It is 
useful for converting rectangular coordinates to polar coordinates.
See Section 8.3.8, “Approximation of Pi” and Section 8.3.10, “Transcendental Instruction Accuracy” for information 
regarding the accuracy of these instructions. 

8.3.8 

Approximation of Pi

When the argument (source operand) of a trigonometric function is within the domain of the function, the argu-
ment is automatically reduced by the appropriate multiple of 2π through the same reduction mechanism used by 

the FPREM and FPREM1 instructions. The internal value of π (3.1415926…) that the x87 FPU uses for argument 

Table 8-8.  TEST Instruction Constants for Conditional Branching

Order

Constant

Branch

ST(0) > Source Operand

4500H

JZ

ST(0) < Source Operand

0100H

JNZ

ST(0) = Source Operand

4000H

JNZ

Unordered

0400H

JNZ