User's Manual

NUMERIC PROGRAMMING EXAMPLES
Cosine Uses Sine Code
To save code space, the cosine function uses most of the sine function code. The relation sin ( I A I +
7r /2) = cos (A) is used to convert the cosine a.rgument into a sine argument. Adding 7r /2 to the angle
is performed by adding 010
2
to the FPREM quotient bits identifying the argument's octant.
It would be very inaccurate to add 7r /2 to the cosine argument if it was very much different
from
7r/2.
Depending on which octant the argument falls in, a different relation will be used in the sine and
tangent functions. The program listings
show which relations are used.
For the tangent function, the ratio produced by
FPTAN will be directly evaluated. The sine function
will use either a sine or cosine relation depending
on which octant the angle fell into. On exit, these
functions will normally leave a divide instruction in progress to maintain concurrency.
If the input angles are of a restricted range, such as from 0 to 45 degrees, then considerable optimiza-
tion
is possible since full angle reduction and octant identification is not necessary.
All three functions begin
by looking at the value given to them. Not a Number (NaN), infinity, or
empty registers must be specially treated. Unnormals need to be converted to normal values before the
FPTAN instruction will work correctly. Denormals will be converted to very small unnormals that do
work correctly for the FPT AN instruction. The sign of the angle is saved to control the sign of the
result.
Within the functions, close attention
was paid to maintain concurrent execution of the 80287 and host.
The concurrent execution will effectively hide the execution time of the decision logic used in the
program.
iAPX286 MACRO A.SSEMBLER 80287 Trignoltletric Functions
SERIES-III iAPX286 MACRO ASSEMBLER XI08 ASSEMBLY OF MODULE TRIO FUNCTIONS
OBJECT MODULE PLACED IN : F3: TRIO. OBJ -
ASSEMBLER INVOKED BY: ASM:!86.96; F3: TRIQ. AP2
LOC OBJ
LINE
1 +1
2
3
4
5
6
7
SOURCE
ttitle("80287 Trignometric Functions")
nama trig_function~
public sine. cosine. tangent
stack
10: 13: 51 OQ/25/83 PAGE
I Ra.erve local space
8
SIIl_2B7 record res1: 1, tend3: I. top: 3. tend:?: 1. tend1: 1, condO: 1.
0000 35CO;!b821A2DAOF
C9FE3F
OOOA OOOOCOFF
9 tc ,..,2: 8
11 code segment el'" public
12
13 Define local constants.
14
15
aven
16 pi_ltuarter dt 3FFEC90FDAA2216BC:235R, Pl/4
17 indefinite dd OFFCOOOOOR , Indefinite special ..... lu.
18 +1 $eJllct
Figure 4-7. Calculating Trigonometric Functions
4-18