User's Manual

iAPX286 MACRO ASSEMBLER
LaC OBJ
002F ODDS
0031 09E8
0033 C3
0034
0034 09E5
0036 'rOOFED
0039 2E082EOOOO
003E 9E
003F 7249
0041 D9C9
0043 13100
0045 7Ee7
0047
0047 D9FB
0049 93
004A 9BDFEO
0040 93
004E F6C704
0051 7544
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0055 OAe9
0057 740F
0059 eOE4FD
Dose BOeFBQ
005F 80C74Q
0062 BODO
0064 Dono
0066 32F8
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006B 7404
0060 DEE9
OOoF EBCE
0071
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09E4
0073 91
0074 9BDFEO
0077 91
0078 0009
007A F6C540
0070 7514
NUMERIC PROGRAMMING EXAMPLES
80287 T'I'ignometric Functions
10: 13: 51 09/25/83 PAGE
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SOURCE
sine:
fstp
fld 1
rot
stCO)
Remove a
Return 1
All ",ork is done as a sine function. By adding PI/2 to the angle
a cosine is converted to a sine. Of c:ourse the angle addition is not
done to the argument but rather to the program logic control ",alues.
fXam
fstsw ax
f!ld pi_quarter
sahf
J'
funnlJ-parameter
Angle is unnormal. normal.
fxch
mov
Jpo
cl,O
5 i ne_z ero_unnorma 1
I Entry point for sine function
Look at the parameter
Look at f!~am status
Get PI/4 ",alue
CF == CO. PF :: C2. ZF == C3
,Jump if emptlJ' NAN. or infinity
denormal.
I ST(1) II: PI/4, steO) angle
; Signal sine
; ,Jump if %ero or unnormal
ST(O) is either a normal or denormal ",alue. Both will work.
Use the fprem instruction to accuratellJ reduce the range of the gi",en
angle to within 0 and PI/4 in magnitude. If fprem cannot reduce the
angle in one shot, the angle is too big to be meaningful, > 2*".62
radians. Any roundoff error in the calculation of the angle given
could completellJ change the result of this function. It is safE'st to
call this verlJ rare c:ase an E'rror.
enter _sine:
fprem
I Reduce angle
xchg ax. b x
fstsw ax
xchg ax. b x
test bh, high(mask cond2l
Jnz angle_too_big
Note that fprem will force a
I denormal to a verlJ small unnormal
Fptan of a very small unnormal
will be the same very small
unnormal. which is correct.
Save old status in EX
Check if reduction was complete
I Quotient in CO. C3. Cl
Put new status in bx
sin(2*N*PI+~) = sin(x)
Set sign flags and test for whic:h eighth of the revolution the
angle fell into
Assert· -PI/4 < st(O) < PI/4
fabs
Dr
J'
cLcl
sine_select
Force the al'gument positive
cond1 bit in bx holds the sign
Test for sine Ol' cosine function
,Jump if sine function
This is a cosine function. Ignol'e the origlnal sign of the angle
and add a G.uarter revolution to the octant id from the fpl'em instruction.
cos (A) :::: sin(A+PI/2) and c:os( :A:) :::: cosCA)
and
add
mov
rol
ah,not high(mask condll
bh, SOH
bh, high (mask con(3)
a}, 0
al,l
bh, al
Turn Off sign of argument
Prepare to add 010 to CO, C3, Cl
status value in ax
Set busy bit so carry out from
C3 will go into the carry flag
Extract carrlJ flag
Put carrlJ flag in low bit
Add carry to CO not changing
Cl flag
See if the argument should be revel'sed, depending on the octant in
which the argument fell during fprem.
test
bh, high(mask condU
Angle was in oct ... nt~ 1.3.5,7.
fsub
Jmp
Angle was in octants 0,2,4,6.
J Reverse angle if' Cl
Invert sense of rotation
o < arg <= PI/4
Test for a zero aT'gument since fptan will not WOT'k if st(O) :::: 0
ftst
Test for zero angle
xchg ax, cx
fstsw ax
c,c'ind3 = 1 if' st(Q) = 0
xchg ax, c x
fstp st( 1)
Remove PI/4
te~t ch,high(mask cond3) I If C3==1. argument is zero
Jnz sine_argument_zero
Figure 4-7. Calculating Trigonometric Functions (Cont'd.)
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